, Volume 1, Issue 2, pp 139-176

Strong minimality of abnormal geodesics for 2-distributions

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We investigate the local length minimality (by theW 1,1- orH 1-topology) of abnormal sub-Riemannian geodesics for rank 2 distributions. In particular, we demonstrate that this kind of local minimality is equivalent to the rigidity for generic abnormal geodesics, and introduce an appropriateJacobi equation in order to computeconjugate points. As a corollary, we obtain a recent result of Sussmann and Liu about the global length minimality of short pieces of the abnormal geodesics.

Partially supported by the Russian Fund for Fundamental Research under grant No. 93-011-1728, and by the International Science Foundation under grant MSD000.