English

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 rr, the projection of strictly singular trajectories to some rr-dimensional manifold must remain within an analytic variety. As a consequence, for rank-2 metabelian distributions, geodesics are of class C1C^1.

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}
}