Metabelian distributions and sub-Riemannian geodesics
Differential Geometry
2024-05-27 v1 Optimization and Control
Abstract
We begin by characterizing metabelian distributions in terms of principal bundle structures. Then, we prove that in sub-Riemannian manifolds with metabelian distributions of rank , the projection of strictly singular trajectories to some -dimensional manifold must remain within an analytic variety. As a consequence, for rank-2 metabelian distributions, geodesics are of class .
Keywords
Cite
@article{arxiv.2405.14997,
title = {Metabelian distributions and sub-Riemannian geodesics},
author = {Enrico Le Donne and Nicola Paddeu and Alessandro Socionovo},
journal= {arXiv preprint arXiv:2405.14997},
year = {2024}
}