Sub-Riemannian Geometry and Geodesics in Banach Manifolds

Sylvain Arguillere

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arXiv · 1601.00827

Sub-Riemannian Geometry and Geodesics in Banach Manifolds

Sylvain Arguillere

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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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Sylvain Arguillere. 2016-01-05. Sub-Riemannian Geometry and Geodesics in Banach Manifolds. https://arxiv.org/abs/1601.00827

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