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Singularités en géométrie sous-riemannienne

Ludovic Sacchelli 1, 2 
2 CaGE - Control And GEometry
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : We investigate the relationship between features of of sub-Riemannian geometry and an array of singularities that typically arise in this context.With sub-Riemannian Whitney theorems, we ensure the existence of global extensions of horizontal curves defined on closed set by requiring a non-singularity hypothesis on the endpoint-map of the nilpotent approximation of the manifold to be satisfied.We apply perturbative methods to obtain asymptotics on the length of short locally-length-minimizing curves losing optimality in contact sub-Riemannian manifolds of arbitrary dimension. We describe the geometry of the singular set and prove its stability in the case of manifolds of dimension 5.We propose a construction to define line fields using pairs of vector fields. This provides a natural topology to study the stability of singularities of line fields on surfaces.
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Submitted on : Thursday, October 11, 2018 - 9:40:19 AM
Last modification on : Wednesday, June 8, 2022 - 12:50:07 PM
Long-term archiving on: : Saturday, January 12, 2019 - 12:38:08 PM


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  • HAL Id : tel-01893068, version 1


Ludovic Sacchelli. Singularités en géométrie sous-riemannienne. Géométrie différentielle [math.DG]. Université Paris Saclay (COmUE), 2018. Français. ⟨NNT : 2018SACLX050⟩. ⟨tel-01893068⟩



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