Almost-Riemannian Geometry on Lie Groups
نویسندگان
چکیده
A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) 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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عنوان ژورنال:
- SIAM J. Control and Optimization
دوره 54 شماره
صفحات -
تاریخ انتشار 2016