HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Almost-Riemannian Geometry on Lie Groups

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [21 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01120535
Contributor : Philippe Jouan Connect in order to contact the contributor
Submitted on : Thursday, October 29, 2015 - 11:26:55 AM
Last modification on : Wednesday, November 3, 2021 - 4:29:38 AM
Long-term archiving on: : Friday, April 28, 2017 - 4:45:17 AM

Files

Article ARS.pdf
Files produced by the author(s)

Identifiers

Citation

Victor Ayala, Philippe Jouan. Almost-Riemannian Geometry on Lie Groups. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, ⟨10.1137/15M1038372⟩. ⟨hal-01120535v2⟩

Share

Metrics

Record views

339

Files downloads

194