Sub-Riemannian Geometry and Geodesics in Banach Manifolds
Copyright policy )Sub-Riemannian Geometry and Geodesics in Banach Manifolds
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.
Mathematics - Differential Geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 510
Mathematics - Differential Geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 510
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