Calculus of Variations and Geometric Measure Theory

D. Barilari - U. Boscain - J. P. Gauthier

On 2-step, corank 2 nilpotent sub-Riemannian metrics

created by barilari on 12 Mar 2012


Published Paper

Inserted: 12 mar 2012
Last Updated: 12 mar 2012

Journal: SIAM, Journal of Control and Optimization
Volume: 50
Number: 1
Pages: 559-582
Year: 2012


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.