Comparison theorems for conjugate points in sub-Riemannian geometry

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 3D left-invariant sub-Riemannian structures.
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Submitted on : Wednesday, March 4, 2015 - 5:51:56 PM
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D. Barilari, L. Rizzi. Comparison theorems for conjugate points in sub-Riemannian geometry. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2016, 22 (2), ⟨10.1051/cocv/2015013⟩. ⟨hal-00931840⟩

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