Issue |
ESAIM: COCV
Volume 22, Number 2, April-June 2016
|
|
---|---|---|
Page(s) | 439 - 472 | |
DOI | https://doi.org/10.1051/cocv/2015013 | |
Published online | 24 March 2016 |
Comparison theorems for conjugate points in sub-Riemannian geometry
1
Université Paris Diderot – Paris 7, Institut de Mathematique de Jussieu, UMR CNRS 7586 – UFR de Mathématiques
davide.barilari@imj-prg.fr
2
CNRS, CMAP École Polytechnique and Équipe INRIA GECO Saclay
Île-de-France, Paris, France
Received:
6
September
2014
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.
Mathematics Subject Classification: 53C17 / 53C21 / 53C22 / 49N10
Key words: Sub-Riemannian geometry / curvature / comparison theorems / conjugate points
© EDP Sciences, SMAI 2016
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