Ludovic Rifford: Geometric control and sub-Riemannian geodesics - Part I

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This will be an introduction to sub-Riemannian geometry from the point of view of control theory. We will define sub-Riemannian structures and prove the Chow Theorem. We will describe normal and abnormal geodesics and discuss the completeness of the Carnot-Carathéodory distance (Hopf-Rinow Theorem). Several examples will be given (Heisenberg group, Martinet distribution, Grusin plane).

Recording during the thematic meeting: "Sub-Riemannian manifolds: from geodesics to hypoelliptic diffusion" the September 01, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent