On 2-step, corank 2 nilpotent sub-Riemannian metrics
Optimization and Control
2011-11-08 v2 Systems and Control
Abstract
In this paper we study the nilpotent 2-step, corank 2 sub-Riemannian metrics that are nilpotent approximations of general sub-Riemannian metrics. We exhibit optimal syntheses for these problems. It turns out that in general the cut time is not equal to the first conjugate time but has a simple explicit expression. As a byproduct of this study we get some smoothness properties of the spherical Hausdorff measure in the case of a generic 6 dimensional, 2-step corank 2 sub-Riemannian metric.
Keywords
Cite
@article{arxiv.1105.5766,
title = {On 2-step, corank 2 nilpotent sub-Riemannian metrics},
author = {Davide Barilari and Ugo Boscain and Jean-Paul Gauthier},
journal= {arXiv preprint arXiv:1105.5766},
year = {2011}
}