Sub-Riemannian Curvature in Contact Geometry |
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Authors: | Andrei Agrachev Davide Barilari Luca Rizzi |
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Institution: | 1.SISSA,Trieste,Italy;2.MI RAS,Moscow,Russia;3.IM SB RAS,Novosibirsk,Russia;4.Institut de Mathématiques de Jussieu-Paris Rive Gauche,Paris,France;5.CMAP école Polytechnique and équipe INRIA GECO Saclay ?le-de-France,Paris,France |
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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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