Sub-Riemannian Geometry and Geodesics in Banach Manifolds

Sylvain Arguillere (1, 2)

1 MMCS - Modélisation mathématique, calcul scientifique
2 ICJ - Institut Camille Jordan

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.

Domaines: Optimisation et contrôle [math.OC]; Géométrie différentielle [math.DG]

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