# COMPARISON THEOREMS FOR CONJUGATE POINTS IN SUB-RIEMANNIAN GEOMETRY

@article{Barilari2016COMPARISONTF, title={COMPARISON THEOREMS FOR CONJUGATE POINTS IN SUB-RIEMANNIAN GEOMETRY}, author={Davide Barilari and Luca Rizzi}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, year={2016}, volume={22}, pages={439-472} }

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 applica- tion, we prove a version of sub-Riemannian Bonnet-Myers theorem and we obtain some new results on conjugate…

## 27 Citations

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