Appears in collections : Sub-Riemannian manifolds : from geodesics to hypoelliptic diffusion / Géométrie sous-riemannienne : des géodésiques aux diffusions hypoelliptiques, Sub-Riemannian manifolds : from geodesics to hypoelliptic diffusion / Géométrie sous-riemannienne : des géodésiques aux diffusions hypoelliptiques

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).