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Pré-Publication, Document De Travail Année : 2015

Sub-Riemannian curvature in contact geometry

Résumé

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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Dates et versions

hal-01160901 , version 1 (04-11-2015)
hal-01160901 , version 2 (08-12-2015)
hal-01160901 , version 3 (21-02-2016)

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Andrei Agrachev, Davide Barilari, Luca Rizzi. Sub-Riemannian curvature in contact geometry. 2015. ⟨hal-01160901v2⟩
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