Podobryaev A. Homogeneous geodesics in sub-Riemannian geometry (abstract)

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Speaker: Alexey Podobryaev

Title: Homogeneous geodesics in sub-Riemannian geometry

Abstract:
We study homogeneous geodesics of sub-Riemannian manifolds, i.e., geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum. We discuss some examples of geodesic orbit sub-Riemannian manifolds (that means all geodesics are homogeneous) and prove that Carnot groups of step more than 2 can not be geodesic orbit. We prove that the geodesic flow for geodesic orbit sub-Riemannian manifold is integrable in non-commutative sense.


Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.