Riemannian and Sub-Riemannian geodesic flows
Differential Geometry
2015-02-24 v1
Abstract
In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of sub-Riemannian metrics on totally geodesic Riemannian submersions. As a consequence we can characterize sub-Riemannian geodesics as the horizontal lifts of projections of Riemannian geodesics.
Cite
@article{arxiv.1502.06018,
title = {Riemannian and Sub-Riemannian geodesic flows},
author = {Mauricio Godoy Molina and Erlend Grong},
journal= {arXiv preprint arXiv:1502.06018},
year = {2015}
}
Comments
12 pages