Hopf-Rinow Theorem of sub-Finslerian geometry
Differential Geometry
2023-02-01 v1
Abstract
The sub-Finslerian geometry means that the metric is defined only on a given subbundle of the tangent bundle, called a horizontal bundle. In the paper, a version of the Hopf-Rinow theorem is proved in the case of sub-Finslerian manifolds, which relates the properties of completeness, geodesically completeness, and compactness. The sub-Finsler bundle, the exponential map and the Legendre transformation are deeply involved in this investigation.
Keywords
Cite
@article{arxiv.2301.13438,
title = {Hopf-Rinow Theorem of sub-Finslerian geometry},
author = {Layth M. Alabdulsada and Laszlo Kozma},
journal= {arXiv preprint arXiv:2301.13438},
year = {2023}
}
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12 pages