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

2011/05/29 by Barilari, Davide, Boscain, Ugo, Gauthier, Jean-Paul · 1 citation
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.1105.5766

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.

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