On 2-step, corank 2 nilpotent sub-Riemannian metrics
  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. 
Davide Barilari (SISSA/ISAS), Ugo Boscain (CMAP), Jean-Paul Gauthier   (LSIS)
math.OC cs.SY