459 research outputs found
Riemannian and Sub-Riemannian geodesic flows
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.Comment: 12 page
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