Riemannian and Sub-Riemannian geodesic flows

Mauricio Godoy Molina; Erlend Grong

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arXiv · 1502.06018

Riemannian and Sub-Riemannian geodesic flows

Mauricio Godoy Molina·Erlend Grong

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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.

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BibTeX RIS

Mauricio Godoy Molina, Erlend Grong. 2015-02-20. Riemannian and Sub-Riemannian geodesic flows. https://arxiv.org/abs/1502.06018

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