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arXiv · 1401.3193

Comparison theorems for conjugate points in sub-Riemannian geometry

Davide Barilari·Luca Rizzi
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Abstract

We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian structures as a special kind of variational problems. In this setting, we identify a class of models, namely linear quadratic optimal control systems, that play the role of the constant curvature spaces. As an application, we prove a version of sub-Riemannian Bonnet-Myers theorem and we obtain some new results on conjugate points for three dimensional left-invariant sub-Riemannian structures.

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Davide Barilari, Luca Rizzi. 2016-05-13. Comparison theorems for conjugate points in sub-Riemannian geometry. https://doi.org/10.1051/cocv%2F2015013

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