Calculus of Variations and Geometric Measure Theory

A. Agrachev - D. Barilari - L. Rizzi

Sub-Riemannian curvature in contact geometry

created by rizzi1 on 17 May 2015
modified on 15 May 2017


Published Paper

Inserted: 17 may 2015
Last Updated: 15 may 2017

Journal: Journal of Geometric Analysis
Year: 2015
Doi: 10.1007/s12220-016-9684-0

ArXiv: 1505.04374 PDF


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.

Keywords: Curvature, sub-Riemannian, contact, comparison