Submersions and curves of constant geodesic curvature

2017/07/17 by Molina, Mauricio Godoy, Grong, Erlend, Markina, Irina
#53C17 #53C20 #53C22 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.05155

Abstract

Considering Riemannian submersions, we find necessary and sufficient conditions for when sub-Riemannian normal geodesics project to curves of constant first geodesic curvature or constant first and vanishing second geodesic curvatures. We describe a canonical extension of the sub-Riemannian metric and study geometric properties of the obtained Riemannian manifold. This work contains several examples illustrating the results.

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