Metric Lines in the Special Euclidean group on the plane
Differential Geometry
2024-12-09 v2
Abstract
The Special Euclidean group on the plane has the left-invariant sub-Riemannian structure. Every sub-Riemannian manifold possesses a Hamiltonian function governing the sub-Riemannian geodesic flow. Two natural questions are: What are the necessary conditions for periodic sub-Riemannian geodesics? What geodesics are the metric lines in SE(2)? We answer both questions, and our method for the second is an alternative proof using the Hamilton-Jacobi theory.
Keywords
Cite
@article{arxiv.2408.13873,
title = {Metric Lines in the Special Euclidean group on the plane},
author = {Y. Wang and S. Ku and A. Bravo-Doddoli},
journal= {arXiv preprint arXiv:2408.13873},
year = {2024}
}