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

Davide Barilari (1) , Ugo Boscain (2) , Jean-Paul Gauthier (3)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 LSIS - Laboratoire des Sciences de l'Information et des Systèmes

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.

Domaines: Optimisation et contrôle [math.OC]

Davide Barilari, Ugo Boscain, Jean-Paul Gauthier. On 2-step, corank 2 nilpotent sub-Riemannian metrics. SIAM Journal on Control and Optimization, 2012, 50 (1), pp.559-582. ⟨hal-00596665v2⟩