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Sub-Riemannian curvature in contact geometry

Abstract : We compare different notions of curvature on contact sub-Riemannian manifolds. In particular we introduce canonical curvatures as the coefficients of the sub-Riemannian Jacobi equation. The main result is that all these coefficients are encoded in the asymptotic expansion of the horizontal derivatives of the sub-Riemannian distance. We explicitly compute their expressions in terms of the standard tensors of contact geometry. As an application of these results, we obtain a sub-Riemannian version of the Bonnet-Myers theorem that applies to any contact manifold.
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Submitted on : Sunday, February 21, 2016 - 10:05:49 AM
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Andrei Agrachev, Davide Barilari, Luca Rizzi. Sub-Riemannian curvature in contact geometry. Journal of Geometric Analysis, 2016, ⟨10.1007/s12220-016-9684-0⟩. ⟨hal-01160901v3⟩



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