Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry
Differential Geometry
2024-04-03 v1
Abstract
This paper explicitly constructs the complete set of optimal sub-Riemannian geodesics starting from a point for certain Carnot groups of step two. These are groups of dimension 2n+1 equipped with a left-invariant distribution of dimension n+1 such that at each point, there is a unique direction defining a nontrivial Lie bracket. A suitable explicit expression of geodesics, together with symmetries of the structure, allows us to identify the cut time and the cut locus by applying the so-called extended Hadamard technique.
Cite
@article{arxiv.2404.01831,
title = {Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry},
author = {Aleš Návrat and Lenka Zalabová},
journal= {arXiv preprint arXiv:2404.01831},
year = {2024}
}