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 by-product 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. © 2012 Society for Industrial and Applied Mathematics.

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

Barilari D.;Boscain U.;
2012

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 by-product 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. © 2012 Society for Industrial and Applied Mathematics.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3401929
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