Riemannian and Sub-Riemannian geodesic flows

20 Feb 2015  ·  Molina Mauricio Godoy, Grong Erlend ·

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. read more

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Differential Geometry