2023/01/31 by Layth M. Alabdulsada, Alabdulsada, Layth M., L. Kozma +1
Physics and Astronomy · #Advanced Differential Geometry Research
paper · pdf · doi:10.48550/arxiv.2301.13438
The sub-Finslerian geometry means that the metric F 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.