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

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.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00596665
Contributor : Davide Barilari <>
Submitted on : Friday, November 4, 2011 - 3:31:13 PM
Last modification on : Tuesday, April 2, 2019 - 2:03:31 AM
Long-term archiving on : Sunday, February 5, 2012 - 2:25:21 AM

Files

000-Corank2-BBG.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00596665, version 2
  • ARXIV : 1105.5766

Citation

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

Share

Metrics

Record views

737

Files downloads

230