On the role of abnormal minimizers in sub-Riemannian geometry

Bernard Bonnard; Emmanuel Trélat

On the role of abnormal minimizers in sub-Riemannian geometry

Optimization and Control 2016-08-16 v1

Authors: Bernard Bonnard , Emmanuel Trélat

Abstract

Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty$ or $C^\omega)$ distribution and $g$ is a smooth metric on $D$ . The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.

Keywords

sub-Riemannian geometry abnormal minimizer Martinet geometry distribution smooth metric

Cite

@article{arxiv.math/0607426,
  title  = {On the role of abnormal minimizers in sub-Riemannian geometry},
  author = {Bernard Bonnard and Emmanuel Trélat},
  journal= {arXiv preprint arXiv:math/0607426},
  year   = {2016}
}

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