Reference : Riemannian and Sub-Riemannian geodesic flow
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Riemannian and Sub-Riemannian geodesic flow
Godoy Molina, Mauricio [University of Bergen > Department of Mathematics]
Grong, Erlend mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Journal of Geometric Analysis
Springer New York LLC
Yes (verified by ORBilu)
New York
[en] Riemannian submersions ; totally geodesic foliations ; sub-Riemannian normal geodesics
[en] 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 result allows us describe the sub-Riemannian geodesic flow on totally geodesic Riemannian foliations in terms of the Riemannian geodesic flow. Also, given a submersion $\pi:M \to B$, we describe when the projections of a Riemannian and a sub-Riemannian geodesic flow in $M$ coincide.
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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