Almost-Riemannian Geometry on Lie Groups
Differential Geometry
2015-11-02 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1503.03040,
title = {Almost-Riemannian Geometry on Lie Groups},
author = {Victor Ayala and Philippe Jouan},
journal= {arXiv preprint arXiv:1503.03040},
year = {2015}
}