Almost-Riemannian Geometry on Lie Groups

Victor Ayala; Philippe Jouan

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arXiv · 1503.03040

Almost-Riemannian Geometry on Lie Groups

Victor Ayala·Philippe Jouan

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Abstract

A simple Almost-Riemmanian Structure on a Lie group G is defined by a linear vector field and dim(G)-1 left-invariant ones. We state results about the singular locus, the abnormal extremals and the desingularization of such ARS's, and these results are illustrated by examples on the 2D affine and the Heisenberg groups.These ARS's are extended in two ways to homogeneous spaces, and a necessary and sufficient condition for an ARS on a manifold to be equivalent to a general ARS on a homogeneous space is stated.

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Victor Ayala, Philippe Jouan. 2015-03-10. Almost-Riemannian Geometry on Lie Groups. https://arxiv.org/abs/1503.03040

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