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.
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Partially supported by the Russian Fund for Fundamental Research under grant No. 93-011-1728, and by the International Science Foundation under grant MSD000.
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Agrachev, A.A., Sarychev, A.V. Strong minimality of abnormal geodesics for 2-distributions. Journal of Dynamical and Control Systems 1, 139–176 (1995). https://doi.org/10.1007/BF02254637
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DOI: https://doi.org/10.1007/BF02254637