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Sub-Riemannian Geometry and Geodesics in Banach Manifolds

Abstract : In this paper, we define and study sub-Riemannian structures on Banach manifolds. We obtain extensions of the Chow-Rashevski theorem for exact controllability, and give conditions for the existence of a Hamiltonian geodesic flow despite the lack of a Pontryagin Maximum Principle in the infinite dimensional setting.
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https://hal.archives-ouvertes.fr/hal-02097140
Contributor : Sylvain Arguillere <>
Submitted on : Thursday, April 11, 2019 - 6:41:22 PM
Last modification on : Thursday, November 5, 2020 - 8:14:01 PM

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Sylvain Arguillere. Sub-Riemannian Geometry and Geodesics in Banach Manifolds. The Journal of Geometric Analysis, Springer, 2019, ⟨10.1007/s12220-019-00184-5⟩. ⟨hal-02097140⟩

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