Seminario de Mecánica Geométrica y Control
Curvature and Jacobi fields in subriemannnian geometry
Ponente: David Iglesias-Ponte (Universidad de La Laguna)Fecha: viernes 07 de mayo de 2021 - 15:30Lugar: Online - zoom.us/j/96739216821?pwd=UDhPYlNzM0M3dXFHUnJRSW92enl1dz09
When dealing with Riemannian geometry, Jacobi fields along geodesics play an important role in the study of conjugate points. Moreover, since they are solutions of the so-called Jacobi equation, they are related with the curvature of the Levi-Civita connection. Considering the Lagrangian of kinetic type associated with the metric, Jacobi fields can be seen to be solutions of the complete lift to the tangent bundle. Using this interpretation, we propose a definition of a Jacobi field in sub-Riemannian geometry, in which the metric tensor is only defined on a sub-bundle, as a solution of the lifted optimal control problem, which would allow us to extract a notion of sub-Riemannian curvature. This is joint work with Roberta Ghezzi, Juan Carlos Marrero and Edith Padrón.