Strong minimality of abnormal geodesics for 2-distributions
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We investigate the local length minimality (by theW1,1- orH1-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.
1991 Mathematics Subject Classification49K30 53C22
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