Title: Strong minimality of abnormal geodesics for 2-distributions
Authors: A.A. Agrachev, A.V. Sarychev
Journal title: J. Dynamical and Control Systems
Year: 1995
Volume: 1
Pages: 139-176
Abstract:

We investigate the local length minimality (by the $$W_{1,1}$$ or $$H_1$$-topology) of abnormal sub-Riemannian geodesics for rank 2 distributions. In particular, we demnstrate that this kind of local minimality is equivalent to the rigidity for generic abnormal geodesics, and introduce an appropriate Jacobi equation in order to compute conjugate points. As a corollary, we obtain a recent resultof Sussmann and Liu about the global length minimality of short pieces of the abnormal geodesics.