English

The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry

Optimization and Control 2010-09-15 v1

Abstract

We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry. We compute estimations of the exponential map which allow us to describe the conjugate locus and the cut locus at a tangency point. We prove that this last one generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set.

Keywords

Cite

@article{arxiv.1009.2612,
  title  = {The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry},
  author = {Bernard Bonnard and Grégoire Charlot and Roberta Ghezzi and Gabriel Janin},
  journal= {arXiv preprint arXiv:1009.2612},
  year   = {2010}
}