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arXiv · 1505.04374

Sub-Riemannian curvature in contact geometry

Andrei Agrachev·Davide Barilari·Luca Rizzi
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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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Andrei Agrachev, Davide Barilari, Luca Rizzi. 2015-05-17. Sub-Riemannian curvature in contact geometry. https://doi.org/10.1007/s12220-016-9684-0

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