Existence theorem for sub-Lorentzian problems
Differential Geometry
2024-05-14 v2 Metric Geometry
Optimization and Control
Abstract
In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We specifically address the case of invariant structures on homogeneous spaces, as the conditions for the existence theorem in this case can be significantly simplified. In particular, it turns out that longest paths exist for any left-invariant sub-Lorentzian structures on Carnot groups.
Cite
@article{arxiv.2401.07975,
title = {Existence theorem for sub-Lorentzian problems},
author = {L. V. Lokutsievskiy and A. V. Podobryaev},
journal= {arXiv preprint arXiv:2401.07975},
year = {2024}
}
Comments
11 pages