menu

links

other_info

This site is under construction. I apologize for any inconvenience. Feel free to contact the webmaster for any correction/sugestion.


A complete list of publications may be found through AMS MathSciNet, and a list of recent preprints through arXiv.org.

selected papers

  • M. de León, J. C. Marrero, E. Martínez: Lagrangian submanifolds and dynamics on Lie algebroids. J. Phys. A: Math. Gen. 38 (2005), R241-R308. (Topical review).
  • M. de León, D. Martín de Diego, A. Santamaría-Merino: Geometric Numerical Integration of Nonholonomic Systems and Optimal Control Problems, European Journal of Control 10 (2004), 520-526.
  • J. Cortés, M. de León, D. Martín de Diego, S. Martínez: Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions. SIAM Journal of Control and Optimization 41 5 (2003), 1389-1412.
  • M. de León, M. Epstein: Continuous distributions of inhomogeneities in liquidcrystal-like bodies. Royal Society of London Proceedings Series A: Math. Phys. Eng. Sci. 457 2014 (2001), 2507-2520.
  • F. Cantrijn, M. de León, D. Martín de Diego: On almost-Poisson structures in nonholonomic mechanics. Nonlinearity 12 3 (1999), 721-737.
  • M. de León, M. Fernández, R. Ibáñez: The canonical spectral sequences for Poisson manifolds. Israel Journal of Mathematics 106 (1998), 133-155.
  • M. de León, M. Epstein: Geometrical Theory of Uniform Cosserat Media. Journal of Geometry and Physics 26 (1998), 127-170.
  • M. de León, D. Martín de Diego: On the geometry of non-holonomic Lagrangian systems. J. Math. Phys. 37 (7) (1996), 3389-3414.
  • F. Cantrijn, M. de León, E. A. Lacomba: Gradient vector fields on cosymplectic manifolds. Journal of Physics A: Math. Gen., 25 (1992), 175-188.
  • L. A. Cordero, M. de León, M. Fernández: Examples of compact non-Kähler almost Kähler manifolds. Proc. Amer. Math. Soc., 95, 2 (1985) 280-286.

preprints

  • Hamiltonian systems in multisymplectic field theory, joint with A. Echevarría-Enríquez, M. Muñoz-Lecanda and N. Román-Roy. Submited to Journal of Geometry and Physics.
  • Nonholonomic lagrangian systems on Lie algebroids, joint with J. Cortés, J.C. Marrero and E. Martínez. Submited to Discrete and Continuous Dynamical Systems - Series A.
  • Towards a Hamilton-Jacobi theory for nonholonomic mechanical systems, joint with D. Iglesias and D. Martín de Diego. Submited to Journal of Physics A: Math. Gen.
  • Geometric Structures in Field Theory, joint with M. McLean, L.K. Norris, A.M. Rey and M. Salgado. Submited to Forschritte für Physik.
  • Characterization of hyperelasticity uniformity, joint with A. Danescu and M. Epstein.
  • Lagrangian submanifolds in multisymplectic geometry, Applications to Hamilton-Jacobi theory, Joint with D. Martín de Diego and Aitor Santamaría).
  • A geometric approach to constrained field theories and optimal control for distributed parameter systems, joint with C. López, J. Marín-Solano, D. Martín de Diego and N. Román-Roy.
  • Geometric Hamilton-Jacobi theory for classical field theories, joint with D. Iglesias, J.C. Marrero and D. Martín de Diego.
  • Hamilton-Jacobi Theory for Higher-Order Mechanical, joint with D. Iglesias, J.C. Marrero and D. Martín de Diego.

papers

2006
  • Semi-discrete variational Mechanics: Some applications of semi-discrete variational integrators to classical field theories. Qualitative Theory of Dynamical Systems. Joint with J.C. Marrero and D. Martín de Diego.
  • A survey on lagrangian mechanics and control on Lie algebroids and groupoids. International Journal of Geometric Methods in Modern Physics, Vol. 3 No. 3(2006), 509-558. Joint with J. Cortés, J.C. Marrero, D. Martín de Diego and E. Martínez.
  • Higher-order Discrete Lagrangian Mechanics. International Journal of Geometric Methods in Modern Physics, Vol. 3 No. 3 (2006), 421-436. Joint with R. Benito and D. Martín de Diego.
2005
  • Geometric aspects of nonholonomic field theories. Reports on Mathematical Physics, 56 (3) (2005), 387-411 Joint with J. Vankerschaver, F. Cantrijn and D. Martín de Diego.
  • Pre-multisymplectic constraint algorithm for field theories. International Journal of Geometric Methods in Modern Physics, Vol. 2 No. 5 (2005), 839-871. Joint with J. Marín-Solano, J.C. Marrero, M. Muñoz-Lecanda and N. Román-Roy.
  • Discrete optimal control theory and symplectic integrators. Adv. Comput. Math. (2005). Joint with D. Martín de Diego and A. Santamaría-Merino.
  • Lagrangian submanifolds and dynamics on Lie algebroids. J. Phys. A: Math. Gen., 38 (2005), R241-R308. (Topical review) Joint with J.C. Marrero and E. Martínez.
2004
  • Classification of material G-structures. Mediterranean Journal of Mathematics, 1 (2004), 375-416.(Con D. Marín.
  • Geometric Numerical Integration of Nonholonomic Systems and Optimal Control Problems. European Journal of Control, 10 (2004), 520-526. Joint with D. Martín de Diego and A. Santamaría-Merino.
  • Symmetries in Field Theory. International Journal of Geometric Methods in Modern Physics, 1 5 (2004), 651-710. Joint with D. Martín de Diego and Aitor Santamaría.
  • A generalization of Chetaev's principle for a class of higher order nonholonomic constraints. Journal of Mathematical Physics, 45 (7) (2004), 2785-2801. Joint with H. Cendra, A. Ibort and D. Martín de Diego.
  • Geometric integrators and nonholonomic mechanics. Journal of Mathematical Physics, 45 (3) (2004), 1042-1064. Joint with D. Martín de Diego and Aitor Santamaría.
  • General symmetries in optimal control. Reports on Mathematical Physics, 53 1 (2004), 55-78. Joint with J. Cortés, D. Martín de Diego and S. Martínez.
2003
  • Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions. SIAM Journal of Control and Optimization, 41 5 (2003), 1389-1412. Joint with J. Cortés, D. Martín de Diego and S. Martínez.
  • On the Computation of the Lichnerowicz-Jacobi Cohomology. Journal of Geometry and Physics 44 (2003), 507-522. Joint with J.C. Marrero, B. Núñez and E. Padrón.
2002
  • Variational integrators and time-dependent lagrangian systems. Reports on Mathematical Physics (2002), 183-192. Joint with D. Martín de Diego.
  • Nonholonomic constraints in classical field theories. Reports on Mathematical Physics (2002), 151-166. Joint with E. Binz, D. Martín de Diego and D. Socolescu.
  • On the geometry of generalized Chaplygin systems. Mathematical Proceedings of the Cambridge Philosophical Society, 132 (2002), 323-351. Joint with F. Cantrijn, J. Cortés and D. Martín de Diego.
  • Characterization of constraints for singular lagrangians on jet bundles. Forschritte für Physik, 50 (2002), 105-169. Joint with J. Marín-Solano, J.C. Marrero, M. Muñoz-Lecanda and N. Román-Roy.
2001
  • Continuous distributions of inhomogeneities in liquid-crystal-like bodies. Royal Society of London Proceedings, Series A: Math. Phys. Eng. Sci. 457 2014 (2001), 2507-2520. Joint with M. Epstein.
  • Duality and modular class of a Nambu-Poisson structure. J. Phys. A: Math. Gen., 34 No 17 (2001), 3623-3650. Joint with R. Ibáñez, J.C. Marrero, B. Núñez, and E. Padrón.
  • Symmetries in vakonomic dynamics. Applications to optimal control. Journal of Geometry and Physics, 38 (2001), 343-365. Joint with J. Cortés and S. Martínez.
  • k-Cosymplectic manifolds and Lagrangian field theory. Journal of Mathematical Physics, 42 (2001), 2092-2104. Joint with E. Merino and M.R. Salgado.
  • On the geometric prequantization of brackets. Revista de la Real Academia de Ciencias, Serie A: Matemáticas. 95 1 (2001), 65-84. Joint with J.C. Marrero and E. Padrón.
  • Geometric version of Carnot's theorem. J. Phys. A: Math. Gen., 34 (2001), 1691-1712. Joint with A. Ibort, E. Lacomba, J.C. Marrero, D.M. de Diego and P. Pitanga.
  • Mechanical systems subjected to generalized nonholonomic constraints. Royal Society of London Proceedings, Series A: Math. Phys. Eng. Sci. 457 2007 (2001), 651-670. Joint with J. Cortés, D. Martín de Diego and S. Martínez.
2000
  • Homogeneity without uniformity: Towards a mathematical foundation of functionally graded materials. International Journal of Solids and Structures, 37 (51)(2000), 7577-7591. Joint with M. Epstein.
  • Vakonomic mechanics versus non-holonomic mechanics: a unified geometrical approach. Journal of Geometry and Physics, 35 (2000), 126-144. Joint with J.C. Marrero and D.M. de Diego.
  • On almost-Poisson structures in nonholonomic mechanics II: the time-dependent framework. Nonlinearity, 13 4 (2000) 1379-1409. Joint with F. Cantrijn, J.C. Marrero and D. M. de Diego.
  • The geometrical theory of constraints applied to the dynamics of vakonomic mechanical systems. The vakonomic bracket. Journal of Mathematical Physics, 41 4 (2000), 2090-2120. Joint with J. Cortés and S. Martínez.
1999
  • Reduction and reconstruction of the dynamics of nonholonomic systems. Journal of Physics A: Mathematics and General, 32 (1999), 8615-8645. Joint with J. Cortés.
  • Leibniz algebroid associated with a Nambu-Poisson structure. Journal of Physics A: Math. Gen., 32 (1999), 8129-8144. Joint with R. Ibáñez, J.C. Marrero and E. Padrón.
  • On the geometry of multisymplectic manifolds. J. Austral. Math. Soc., (Series A) 66 (1999), 303-330. Joint with F. Cantrijn and L. A. Ibort.
  • Dirac brackets in constrained dynamics. Forschritte für Physik, 47 5 (1999), 459-492. Joint with A. Ibort, J.C. Marrero and D.M. de Diego.
  • On almost-Poisson structures in nonholonomic mechanics. Nonlinearity, 12 3 (1999), 721-737. Joint with F. Cantrijn and D.M. de Diego.
  • Reduction of constrained systems with symmetry. Journal of Mathematical Physics, 40 2 (1999), 795-820. Joint with F. Cantrijn, J.C. Marrero and D. M. de Diego.
1998
  • A canonical differential complex for Jacobi manifolds. Michigan Math. J., 45 (1998), 547-579. Joint with Domingo Chinea and Juan C. Marrero.
  • Conservation laws and symmetry in economic growth models: a geometrical approach. Extracta Mathematicae, 13 3 (1998), 335-348. Joint with D.M. de Diego.
  • he canonical spectral sequences for Poisson manifolds. Israel Journal of Mathematics, 106 (1998), 133-155. Joint with M. Fernández and R. Ibañez.
  • Coeffective and de Rham cohomologies of symplectic manifolds. Journal of Geometry and Physics, 27 (1998), 281-296. Joint with Marisa Fernández and Raúl Ibáñez.
  • Coeffective and de Rham cohomologies on almost contact manifolds. Differential Geometry and Its Applications, 8 (1998), 285-303. Joint with Marisa Fernández and Raúl Ibáñez.
  • On a smooth geometric approach to the dynamics of media with microstructure. C.R. Acad. Sc. Paris, t. 326, Série II b, (1998), 227-232. Joint with Ernst Binz and Dan Socolescu.
  • Geometrical Theory of Uniform Cosserat Media. Journal of Geometry and Physics, 26 (1998), 127-170. Joint with M. Epstein.
  • Reduction of Nambu-Poisson and generalized Poisson manifolds. Reports on Mathematical Physics, Vol. 42, No. 1-2 (1998), 71-90. Joint with Raúl Ibáñez, Juan C. Marrero and David Martín de Diego.
  • Reduction of Nonholonomic Mechanical Systems with Symmetries. Reports on Mathematical Physics, Vol. 42, No. 1-2 (1998), 25-45. Joint with F. Cantrijn, J.C. Marrero and D. M. de Diego.
  • Geometric formulation of mechanical systems subjected to time-dependent onesided constraints. Journal of Physics A: Mathematics and Gen., 31 (1998), 2655-2674. Joint with A. Ibort, E.A. Lacomba, J.C. Marrero, D.M. de Diego and P. Pitanga.
  • On uniformity of shells. Int. J. of Solids and Structures, Vol. 35, No. 17 (1998), 2173-2182. Joint with Marcelo Epstein.
  • Hamiltonian systems on k-cosymplectic manifolds. Journal of Mathematical Physics, 39 (1998), 876-893. Joint with E. Merino, J.A. Oubiña, P.R. Rodrigues and M.R. Salgado.
  • Nambu-Jacobi and generalized Jacobi manifolds. J. Phys. A: Math. Gen., 31 (1998), 1267-1286. Joint with R. Ibáñez, J.C. Marrero and E. Padrón.
  • Homology and cohomology of generalized Poisson manifolds. J. Phys. A: Math. Gen., 31 (1998), 1253-1266. Joint with Raúl Ibáñez and Juan C. Marrero.
1997
  • Compact cosymplectic manifolds of positive constant -sectional curvature. Rendiconti di Matematica, Serie VII, Vol. 17 (1997), 607-625. Joint with J. C. Marrero.
  • Spectral sequences on Sasakian and cosymplectic manifolds. Houston Journal of Mathematics, 23 (4) (1997), 631-649. Joint with D. Chinea and J. C. Marrero.
  • Stable almost cotangent structures. Bollettino Unione Matematica Italiana, (7) 11-B (1997), 509-529. Joint with E. Merino, J. A. Oubiña and M. Salgado.
  • On the geometric quantization of Jacobi manifolds. Journal of Mathematical Physics, 38 (12) (1997), 6185-6213. Joint with Juan C. Marrero and Edith Padrón.
  • A Nomizu's theorem for the coeffective cohomology. Mathematische Zeitschrift, 226 (1997), 11-23. Joint with M. Fernández and R. Ibáñez.
  • Lichnerowicz-Jacobi cohomology. Journal of Physics A: Math. Gen., 30 (1997), 6029-6055. Joint with Juan C. Marrero and Edith Padrón.
  • H-Chevalley-Eilenberg cohomology of a Jacobi manifold and Jacobi-Chern class. Comptes Rendu Acad. Sc. Paris, Série I, t. 325 n. 4 (1997), 405-410. Joint with Juan C. Marrero and Edith Padrón.
  • Mechanical systems subjected to impulsive constraints. Journal of Physics A: Math. Gen., 30 (1997), 5835-5954. Joint with Alberto Ibort, Ernesto A. Lacomba, David Martín de Diego and Paulo Pitanga.
  • Coisotropic and Legendre-Lagrangian submanifolds and conformal Jacobi morphisms. J. Phys. A: Math. Gen., 30 (1997), 5427-5444. Joint with Raúl Ibáñez, Juan C. Marrero and David Martín de Diego.
  • A constraint algorithm for singular Lagrangians subjected to non-holonomic constraints. J. Math. Phys., 38 (6) (1997), 3055-3062. Joint with David M. de Diego.
  • Dynamics of generalized Poisson and Nambu-Poisson brackets. J. Math. Phys., 38 (5) (1997), 2332-2344. Joint with Raúl Ibáñez, Juan C. Marrero and David Martín de Diego.
  • Mechanical systems with non-linear constraints. International Journal of Theoretical Physics, 36 (4) (1997), 973-989. Joint with Juan C. Marrero and David Martín de Diego.
  • Reduction of Jacobi manifolds. Journal of Physics A: Math. Gen., 30 (1997), 2783-2798. Joint with Giuseppe Marmo and Luis A. Ibort.
  • R2n+1 is a universal contact manifold for reduction. Journal of Physics A: Math. Gen., 30 (1997), 1605-1611. Joint with J.C. Marrero and Gijs M. Tuynmann.
  • Non-holonomic Lagrangian systems in jet manifolds. Journal of Physics A: Math. and Gen., 30 (1997), 1167-1190. Joint with Juan C. Marrero and David M. de Diego.
  • Lichnerowicz-Jacobi cohomology of Jacobi manifolds. Comptes Rendu Acad. Sc. Paris, Série I, 324 (1997), 71-76. Joint with Juan C. Marrero and Edith Padrón.
1996
  • Non-holonomic constrained systems as implicit differential equations. Rend. Sem. Mat. Univ. Pol. Torino, Vol. 54, 3 (1996), 295-317. Joint with A. Ibort, G. Marmo and D. Martín de Diego.
  • Hamiltonian structures on multisymplectic manifolds. Rend. Sem. Mat. Univ. Pol. Torino, Vol. 54, 3 (1996), 225-236. Joint with A. Ibort and F. Cantrijn.
  • Uniformity and homogeneity of elastic rods, shells and Cosserat three-dimensional bodies. Archivum Mathematicum (Brno), 32 (4) (1996), 267-280. Joint with M. Epstein)
  • Solving non-holonomic Lagrangian dynamics in terms of almost product structures. Extracta Mathematicae, 11 2 (1996), 325-347. Joint with David M. de Diego.
  • Uniformity and homogeneity of deformable surfaces. C. R. Acad. Sci. Paris, 323, Série IIb (1996), 579-584. Joint with M. Epstein.
  • Time-dependent constrained hamiltonian systems and Dirac brackets. Journal of Physics A: Math. Gen., 29 (1996) 6843-6859. Joint with D. M. de Diego and J. C. Marrero.
  • Prequantization of Poisson manifolds and Jacobi structures. Journal of Physics A: Math. Gen., 29 (1996), 6313-6324. Joint with Domingo Chinea and Juan C. Marrero.
  • Homogeneity conditions for generalized Cosserat media. Journal of Elasticity, 43 (1996), 189-201. Joint with M. Epstein.
  • A universal model for cosymplectic manifolds. Journal of Geometry and Physics, 20 (1996), 77-86. Joint with Gijs Tuynman.
  • The constraint algorithm in the jet formalism. Differential Geometry and Its Applications, 6 (1996) 275-300. Joint with Jesús Marín and Juan C. Marrero.
  • The canonical double complex for Jacobi manifolds. C. R. Acad. Sci. Paris, t. 323, Série I (1996), 637-642. Joint with D. Chinea and J. C. Marrero.
  • On the geometry of non-holonomic Lagrangian systems. J. Math. Phys., 37 (7) (1996), 3389-3414. Joint with David M. de Diego.
  • A six dimensional compact symplectic solvmanifold without Kähler structures. Osaka Journal of Mathematics, 33 (1) (1996), 19-35. Joint with M. Fernández and M. Saralegui.
  • On frames defined by horizontal spaces. Czechoslovak Math. J., 46 (121) no.2 (1996), 241-248. Joint with E. Ortacgil.
  • Poisson cohomology and canonical homology of Poisson manifolds. Archivum Mathematicum (Brno), Tomus 32, 1 (1996), 29-56. Joint with M. Fernández and R. Ibañez.
  • Symmetries and constants of the motion for singular Lagrangian systems. International Journal of Theoretical Physics., 35, 5 (1996), 975-1011. Joint with David M. de Diego.
  • Harmonic cohomology classes and the first spectral sequence for compact Poisson manifolds. C. R. Acad. Sci. Paris, 322, Série I (1996), 673-678. Joint with M. Fernández and R. Ibáñez.
  • The geometry of uniformity in second-grade elasticity. Acta Mechanica, 114 1 (1996), 217-224. Joint with M. Epstein.
1995
  • A global characterization of jet bundles of p1-velocities and covelocities. Annales de la Faculté des Sciences de Toulouse, Vol. 4, no. 1 (1995), 61-75. Joint with E. Merino, J. A. Oubiña and M. Salgado.
  • Almost product structures and Poisson reduction of presymplectic systems. Extracta Mathematicae, 10 1 (1995), 37-45. Joint with David M. de Diego.
  • A new look at degenerate Lagrangian dynamics from the viewpoint of almost product structures. J. Phys. A: Math. Gen., 28 (1995), 4951-4971. Joint with David M. de Diego and Paulo Pitanga.
  • Symmetries and constants of the motion for higher order Lagrangian systems. J. Math. Phys., 36, (8) (1995), 4138-4161. Joint with David M. de Diego.
  • Characterization of higher-order tangent bundles. Beiträge zur Algebra und Geometrie, 36, 1 (1995), 73-87. Joint with J. A. Oubiña and M. Salgado.
  • Coeffective cohomology on cosymplectic manifolds. Bull. Sci. math., 119 (1) (1995), 3-20. Joint with D. Chinea and J. C. Marrero.
1994
  • Classification of symmetries for higher order Lagrangian systems II: the non-autonomous case. Extracta Mathematicae, 9 (2) (1994), 111-114. Joint with D. Martín de Diego.
  • Symplectic reduction of higher order Lagrangian systems with symmetry. J. Math. Phys., 35 (12), (1994), 6546-6556. Joint with P. R. Rodrigues and Paulo Pitanga.
  • Integrable Almost s-Tangent Structures. Rendiconti di Matematica, Serie VII, 14 (4) (1994), 609-623. Joint with J. A. Oubiña and M. Salgado.
  • A characterization of tangent and stable tangent bundles. Annales de l'Institut Henri Poincaré: Physique Theorique, 61, 1 (1994), 1-15. Joint with E. Merino, J. A. Oubiña and M. Salgado.
  • Nonautonomous Submersive Second-Order Differential Equations and Lie Symmetries. International Journal of Theoretical Physics, 33, 8 (1994), 1759-1781. Joint with David M. de Diego.
  • Invariants of Lagrangians and their classifications. Journal of Mathematical Physics, 35 (9) (1994), 4568-4593. Joint with Jacek D┬Şebecki, Jacek Gancarzewicz and W lodzimierz Mikulski.
  • Material bodies of higher grade. Comptes Rendus Acad. Sc. Paris, 319, Série I, (1994), 615-620. Joint with M. Epstein.
  • The constraint algorithm for time-dependent Lagrangians. Journal of Mathematical Physics., 35 (7) (1994), 3410-3447. Joint with D. Chinea and J. C. Marrero.
  • Classification of symmetries for higher order Lagrangian systems. Extracta Mathematicae, 9 (1) (1994), 32-36. Joint with David Martín de Diego.
  • Compact cosymplectic manifolds of positive constant '-sectional curvature. Extracta Mathematicae, 9 (1) (1994), 28-31. Joint with Juan C. Marrero.
  • On the coeffective cohomology of compact symplectic manifolds. C. R. Acad. Sci. Paris, 318, Série I, (1994), 231-236. Joint with L.C. de Andrés, M. Fernández, R. Ibañez and J. Mencía.
1993
  • On the integrability of second order G-structures with applications to continuous theories of dislocations. Reports on Mathematical Physics, 33 (3) (1993), 419-436. Joint with M. Epstein.
  • Topology of cosymplectic manifolds. Journal de Mathématiques Pures et Appliquées, 72 (6), (1993), 567-591. Joint with D. Chinea and J. C. Marrero.
  • Cosymplectic reduction for singular momentum maps. Journal of Physics A: Math. Gen., 26 (1993), 5033-5043. Joint with Martín Saralegi.
  • Stability of invariant foliations on almost contact manifolds. Publ. Math. Debrecen, 43 / 1-2 (1993), 41-52. Joint with D. Chinea and J. C. Marrero.
  • Constrained time-dependent Lagrangian systems and Lagrangian submanifolds. J. Math. Phys., 34 (2) (1993), 622-644. Joint with J. C. Marrero.
  • p-Almost cotangent structures. Bollettino Unione Matematica Italiana, (7) 7-A (1993), 97-107. Joint with I. Méndez and M. Salgado.
1992
  • Some six-dimensional compact symplectic and complex solvmanifolds. Rendiconti di Matematica e delle sue aplicazioni, Serie VII, Volume 12, (1992), 59-67. Joint with L. C. de Andrés, M. Fernández and J. Mencía.
  • The inverse problem of Lagrangian dynamics for higher-order differential equations. A geometrical approach. Inverse Problems, 8, 4 (1992), 525-540. Joint with P. R. Rodrigues.
  • Higher-Order Mechanical Systems with Constraints. International Journal of Theoretical Physics, 31 (7) (1992), 1303-1313. Joint with P. R. Rodrigues.
  • Existence of p-almost tangent structures. Czecoslovak Mathematical Journal, 42 (117) (1992), 225-234. Joint with L. A. Cordero, I. Méndez and M. Salgado.
  • Almost s-Tangent Manifolds of Higher Order. Pacific Journal of Mathematics, 154 2 (1992), 201-213. Joint with J. A. Oubiña, P.R. Rodrigues and M. Salgado.
  • Gradient vector fields on cosymplectic manifolds. Journal of Physics A: Math. Gen., 25 (1992), 175-188. Joint with F. Cantrijn and E. A. Lacomba.
1991
  • Symplectic and cosymplectic foliations on cosymplectic manifolds. Publications de l'Institut Mathématique, 50 (64), (1991), 163-169. Joint with D. Chinea and J.C. Marrero.
  • Second order differential equations and degenerate Lagrangians. Rendiconti di Matematica e delle sue aplicazioni, Ser. VII, vol. 11 (1991), 715-728. Joint with P. R. Rodrigues.
  • Locally conformal cosymplectic manifolds and time-dependent Hamiltonian systems. Comment. Math. Univ. Carolinae, 32, 2 (1991), 383-387. Joint with D. Chinea and J. C. Marrero.
  • Connections on tangent bundles of higher order associated to regular Lagrangians. Geometriae Dedicata, 39, (1991), 17-28. Joint with L. C. de Andrés and P. R. Rodrigues.
  • Integrable p-almost tangent manifolds and tangent bundles of p1-velocities. Acta Mathematica Hungarica, 58 (1-2) (1991), 45-54. Joint with I. Méndez and M. Salgado.
1990
  • Almost contact structures and time-dependent Lagrangian systems. Portugaliae Mathematica, 47, 2 (1990), 115-130. Joint with P. R. Rodrigues.
  • A remark on compact symplectic manifolds not admitting complex structures. Archivum Mathematicum (Brno), 26, 1 (1990), 49-54. Joint with M. Fernández e I. Rozas.
1989
  • Compact almost contact solvmanifolds admitting neither Sasakian nor cosymplectic structures. Riv. Mat. Univ. Parma, (4) 15 (1989), 105-110.
  • Compact symplectic four dimensional manifolds not admitting polarizations. Comment. Math. Univ. Carolinae, 30, 4 (1989), 789-793. Joint with M. Fernández.
  • Connections on tangent bundles of higher order. Demonstratio Mathematica, XXII, 3 (1989), 607-632. Joint with L. C. de Andrés and P. R. Rodrigues.
  • Sur la reduction de systémes lagrangiens dégénérés d'ordre supérieur. C. R. Acad. Sci. Paris, série I, 309 (1989), 363-366. Joint with A. Giraldo and P. R. Rodrigues.
  • Examples of stable compact symplectic foliations on compact symplectic manifolds. Portugaliae Mathematica, 46 (4) (1989), 391-399.
  • Lagrangian submanifolds and higher-order mechanical systems. J. Phys. A: Math. Gen. 22, (1989) 3809-3820. Joint with E. Lacomba.
  • Compact symplectic four solvmanifolds without polarizations. Annales de la Faculté des Sciences de Toulouse, vol. X. 2 (1989), 193-198. Joint with L. A. Cordero, M. Fernández and M. Saralegui.
  • nk-Almost Tangent Structures and the Hamiltonization of Higher Order Field Theories. J. Math. Phys., 30 (6) (1989), 1351-1353. Joint with P. R. Rodrigues.
1988
  • Hamiltonian structures and Lagrangian field theories on jet bundles. Bol. Acad. Galega de Ciencias, VII (1988), 69-81. Joint with P. R. Rodrigues.
  • Regular p-almost cotangent structures. J. Korean Math. Soc., 25, 2 (1988), 273-287. Joint with I. Méndez and M. Salgado.
  • Prolongation of G-structures to the frame bundle of second order. Publications Mathematicae (Debrecen), 35 (1988) 21-36. Joint with M. Salgado.
  • Les sous-variétés lagrangiennes dans la dynamique d'ordre supérieur. C. R. Acad. Sci. Paris, série II, 464 (1988) 1137-1139. Joint with E. Lacomba.
  • p-Almost tangent structures. Rend. Circ. Mat. Palermo, Serie II, Tomo XXXVII (1988), 282-294. Joint with I. Méndez and M. Salgado.
  • Dynamical connections and non-autonomous Lagrangian systems. Annales de la Faculté des Sciences de Toulouse, IX, no. 2 (1988), 171-181. Joint with P. R. Rodrigues.
  • Degenerate Lagrangian systems and their associated dynamics. Rendiconti di Matematica e delle sue aplicazioni, Ser. VII, vol. 8 (1988), 105-130. Joint with P. R. Rodrigues.
  • Tensor fields and connections on cross-sections in the frame bundle of second order of a parallelizable manifold. Publications de l'Institut Mathematique, 43 (57) (1988) 143-154. Joint with M. Salgado.
1987
  • Productos de Massey e Variedades Simplécticas non Kählerianas. Boletin Acad. Galega de Ciencias, Vol. VI (1987) 137-164. Joint with L. A. Cordero, M. Fernández and A. Gray.
  • Comments on the canonical formalism on time-dependent higher order Lagrangians. Revista Colombiana de Matemáticas, vol. XXI (1987) 47-64. Joint with P. R. Rodrigues.
  • A contribution to the global formulation of the higher order Poincaré-Cartan form. Letters in Mathematical Physics, 14, 4 (1987) 353-362. Joint with P. R. Rodrigues.
  • Second order differential equations and non-conservative Lagrangian mechanics. J. Phys. A: Math. Gen., 20 (1987) 5393-5396. Joint with P. R. Rodrigues.
  • Diagonal prolongations of G-structures to the frame bundle of second order. Annalele Universitatii Bucuresti, XXXIV (1987) 40-51. Joint with M. Salgado.
  • On the quaternionic Heisenberg group. Bollettino U. M. I., (7) 1-A (1987) 31-37. Joint with L. A. Cordero and M. Fernández.
  • Examples of compact complex manifolds with no Kähler structure. Portugaliae Mathematica, 44, 1 (1987) 49-62. Joint with L. A. Cordero and M. Fernández.
  • Lifts of derivations to the frame bundle. Czechoslovak Math. J., 37 (112) (1987) 42-50. Joint with M. Salgado.
  • Connections of order k on M and associated polynomial structures on TkM. An. Stiint. Univ. Al. I. Cuza Iasi, XXXIII, 3 (1987) 267-276. Joint with I. Méndez and M. Salgado.
1986
  • f-structures on the frame bundle of a Riemannian manifold. Riv. Mat. Univ. Parma, (4), 12 (1986) 257-262. Joint with L. A. Cordero.
  • Diagonal lifts of tensor fields to the frame bundle of second order. Acta Sc. Math., 50 (1986) 67-86. Joint with M. Salgado.
  • Compact locally conformal Kähler manifolds. Geometriae Dedicata, 21 (1986) 187-192. Joint with L. A. Cordero and M. Fernández.
  • Some properties of the holomorphic sectional curvature of the tangent bundle. Rendiconti Seminario Facoltá Scienze Universitá Cagliari, vol. 56, Fasc. 1 (1986) 11-19. Joint with M. Fernández.
  • Lifts of derivations to the tangent bundle of pr-velocities. J. Korean Math. Soc., 23, 2 (1986) 135-140. Joint with M. Salgado.
  • On the curvature of the induced Riemannian metric on the frame bundle of a Riemannian manifold. J. Math. pures et appl., 65 (1986) 81-91. Joint with L. A. Cordero.
  • Prolongation of G-structures to the frame bundle. Ann. Mat. pura Appl. (IV), CXLII (1986) 123-141. Joint with L. A. Cordero.
  • On the differential geometry of the frame bundle. Rev. Roumaine Math. Pures Appl., 31, 1 (1986) 9-27. Joint with L. A. Cordero.
1985
  • Sur une conjecture de Thurston. C. R. Acad. Sci. Paris, série I, 301 (1985) 771.
  • Examples of compact almost contact manifolds admitting neither Sasakian nor cosymplectic structures. Atti Sem. Mat. Fis. Univ. Modena, XXXIV (1985-86) 43-54. Joint with L. A. Cordero and M. Fernández.
  • On the geometry of the tangent bundle of order 2. Analele Universitatii Bucuresti, XXXIV (1985) 40-48. Joint with E. Vázquez Abal.
  • Formalisme hamiltonien symplectique sur les fibrés tangents d'ordre supérieur. C. R. Acad. Sci. Paris, série II, 301 (1985) 103-106. Joint with P. R. Rodrigues.
  • Examples of compact non-Kähler almost Kähler manifolds. Proc. Amer. Math. Soc., 95, 2 (1985) 280-286. Joint with L. A. Cordero and M. Fernández.
  • G-structures on the frame bundle of second order. Riv. Mat. Univ. Parma, (4), 11 (1985) 161-179. Joint with M. Salgado.
  • Almost tangent structures in bundles spaces over almost s-tangent manifolds. Bull. Math. Soc. Sci. Math. R. S. Roumanie, 29, (77), 3 (1985) 245-254. Joint with J. A. Oubiña.
1984
  • A family of non-Kählerian quaternionic manifolds. Bol. Acad. Galega de Ciencias, III (1984) 57-68. Joint with L. A. Cordero and M. Fernández.
  • The dJr -cohomology on the tangent bundle of order k. An. Stiint. Univ. Al. I. Cuza Iasi, XXX, 5 (1984) 69-74.
  • Projectable Derivation Laws and Connections on the Tangent Bundle of Order 2. Indian Journal of Mathematics, 26 (1984) 65-74.
  • Prolongations of vector-valued differential forms to the frame bundle. J. Korean Math. Soc., 21, No. 2 (1984) 183-206. Joint with L. A. Cordero.
  • Horizontal lifts of connections to the frame bundle. Bollettino U. M. I., (6) 3-B (1984) 223-240. Joint with L. A. Cordero.
  • Existence and integrability conditions of (k-1,k-1)-structures on (k+1)n-dimensional manifolds. Rev. Roumaine Math. Pures Appl., 29, 6 (1984) 479-488.
1983
  • A characterization of geodesics of second order. Bol. Acad. Galega de Ciencias, II (1983) 103-106. Joint with M. Salgado.
  • Tensor fields and connections on cross-sections in the frame bundle of a parallelizable manifold. Riv. Mat. Univ. Parma, (4), 9 (1983) 433-445. Joint with L. A. Cordero.
  • Prolongations of linear connections to the frame bundle. Bull. Austral. Math. Soc., 28 (1983) 367-381. Joint with L. A. Cordero.
  • Lifts of tensor fields to the frame bundle. Rend. Circ. Mat. Palermo, XXXII (1983) 236-271. Joint with L. A. Cordero.
1982
  • Some examples of manifolds endowed with an almost complex and an almost tangent structure. Bol. Acad. Galega de Ciencias, I (1982) 95-101.
  • Transformation de Legendre pour les systémes lagrangiens régulieurs d'ordre supérieur. C. R. Acad. Sci. Paris, série I, 295 (1982) 123-125.
  • Systémes lagrangiens régulieurs d'ordre supérieur. C. R. Acad. Sci. Paris, série I, 294 (1982) 451-453.
1981
  • Sprays et connexions sur les fibrés tangents d'ordre supérieur. C. R. Acad. Sci. Paris, série I, 293 (1981) 51-54. Joint with C. Villaverde.
  • Calcul differéntielle sur les fibrés tangents d'ordre supérieur. C. R. Acad. Sci. Paris, série I, 292 (1981) 881-884. Joint with C. Villaverde.
  • Connections and f-structures on T2M. Kodai Math. J., 4 (1981) 189-216.

books

  • M. de León, P. R. Rodrigues: Generalized Classical Mechanics and Field Theory. North-Holland Mathematics Studies, 112, North-Holland, Amsterdam, 1985.
  • M. de León, P. R. Rodrigues: Methods of Differential Geometry in Analytical Mechanics. North-Holland Mathematics Studies, 158, North-Holland, Amsterdam, 1989.
  • L. A. Cordero, C. T. J. Dodson, M. de León: Geometry of Frame Bundles. Mathematics and Its Applications, Kluwer Academic Publishers, Dordrech, 1989.
  • Fotografiando las Matemáticas, Carroggio, Barcelona, 2000. Editor.

popularization and opinion

2007
  • Matemáticas en Secundaria: las ensenamos adecuadamente? Revista del Colegio de Doctores y Licenciados (2007).
  • Organization of the Congress. Proceedings of the ICM2006, European Mathematical Society Publishing House, vol. I (2007), 13-21.
  • El Congreso Internacional de Matemáticos ICM2006 Madrid. Boletín de la Sociedad de Estadística e Investigación Oúrativa volumen 23, n┤umero 1 (2007), 2-4.
  • Las matemáticas: instrumento de paz, cooperación y desarrollo. Epsilón (2007).
2006
  • Un Congreso para la historia de las matemáticas espanolas. Matematicalia, Editorial del Vol. 2, no. 4 (oct. 2006).
  • El Congreso Internacional de Matemáticos ICM2006 Madrid. La Gaceta de la RSME Vol. 9 n o 3 (2006), 615-628,
  • Doce días para recordar. Suma 53 (2006), 120-124.
  • Los finlandeses y la sociedad de la información. El País, 31 de mayo de 2006.
2005
  • ICM2006 Madrid: The Spanish Mathematical Fiesta. Notices A.M.S. (2005).
  • Celebrando las matemáticas: El Congreso Internacional de los Matemáticos de Madrid. Matematicalia, Vol. 1, no. 4 (dic. 2005).
  • El Comité Español de Matemáticas (CeMAT): vertebrando las matemáticas españolas. Matematicalia, 2005.
  • Monográfico Constantes de la Naturaleza, Ciencia Digital.
  • Matemáticas y el CSIC: El reencuentro. Bol. Soc. Mat. Apl. 31 (2005), 17-22.s
  • Las Matemáticas son un arma cargada de futuro. Matematicalia, Vol. 1, No. 1, 2005.
  • La presencia de las matemáticas en España. Padres y Madres de Aúmnos, CEAPA, n┤umero 82, Abril-mayo 2004, 38-41. (Con Tomás Recio).
  • Debemos saber, sabremos. El País, 6 de abril de 2005.
2004
  • Matemática Aplicada en España: Presente y Futuro. La Gaceta de la RSME, Vol. 7, 3 (2004), 665-677. Publicado también en Bol. Soc. Mat. Apl.. (Con E. Zuazua).
  • Los jugadores de ecuaciones y la I+D+i. El País, 3 de noviembre de 2004.
  • Confederación de Sociedades Científicas de España: una apuesta por la vertebración de la Ciencia. Acta Científica y Tecnológica 8 (2004), p. 13.
  • La Internacional Matemática. La larga y tortuosa historia de la Unión Matemática Internacional. Bol. Soc. Mat. Apl. 27 (2004), 95-103.
2002
  • A Internacional Matemática. Gamma 2 (2002), 95-100.
  • La Educación Secundaria en el nuevo marco legal: Realidad actual y perspectivas. Ministerio de Educación, Cultura y Deporte, 2002.
  • La recuperación de las Matemáticas en el CSIC: una prioridad para la ciencia española. Real Academia de Ciencias, Sesión de 30 de mayo de 2002.
2001
  • La situación de la enseñanza de las matemáticas: un documento inicial. La Gaceta de la Real Sociedad Matemática Española, Vol. 4, no. 3 (2001), 499-509. (Con R. Crespo, S. González, S. Guerrero, T. Recio, E. Zuazua).
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 4, no. 1 (2001), 279-291. (Con Francisco A. González Posada).
  • Las matemáticas en España, Mundo Científico, no 219 (2001), 46-53. (Con J.L. Fernández).
2000
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 3, no. 3 (2000), 575-584. (Con Francisco A. González Posada).
  • Las claves matemáticas del desarrollo. Ciencia Digital, Diciembre 2000, no 15.
  • Panorama de las Matemáticas en España. Nueva Revista de Política, Cultura y Arte, no 72 (2000), 112-114.
  • Mirando hacia atrás: Aproximación a la Historia de las Matemáticas en España. La Gaceta de la Real Sociedad Matemática Española, Vol. 3, no. 2 (2000), 363-370. (Con Francisco A. González Posada).
  • Las revistas matemáticas como creadoras de vocabulario. Encuentro sobre la Lengua Española en las Ciencias (Física, Química y Matemáticas) Valladolid, 26-27 Abril 2000. La Gaceta de la Real Sociedad Matemática Española, Vol. 3, no. 2 (2000), 167-172.
  • Los problemas del nuevo milenio, Mundo Científico, no 218 (2000), 58-63. (Con J.L. Fernández).
  • Las sociedades matemáticas. En Números (número especial, Vol. 43 y 44), (2000), pp. 73-76 y en Editorial Nivola, Madrid, 2000.
  • La divulgación: Una asignatura pendiente de las sociedades matemáticas. Ciencia Digital, 14-marzo-2000.
1999
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 2, no. 3 (1999), 583-587.
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 2, no. 2 (1999), 389-393.
  • Informe sobre las Matemáticas y el CSIC. Comisión Asesora: I. Díaz, J.L. Fernández, A. Ibort, M. de León, S. Xambó. (1999).
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 2, no. 1 (1999), 175-176.
1998
  • Las Matemáticas y el CSIC. Jornadas Científicas ''El futuro de la Ciencia y el CSIC'', Abril, 1998. API CSIC, Madrid, 1999, pp. 61-68.
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 1, no. 3 (1998), 489-496.
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 1, no. 2 (1998), 293-306.
  • Mirando hacia atrás. La Gaceta de la Real Sociedad Matemática Española, Vol. 1, no. 1 (1998), 129-134.