1.1) Differential geometry and Riemannian geometry
Integration: Orientation, Integration of a volume form, Stokes theorem. Haar measure on a Lie group. De Rham cohomology: Definition and examples, Poincaré duality, Betti numbers. Hodge theory: Operator Hodge, Outdoor Differential and his deputy, and Laplacian values on RxR varieties Sphere Formula Bochner-Weitzenböck, stiffness results.
1.2) Sub-riemannian manifold. Existence of Riemannian metrics in, generating distributions, not generating cyclic distributions nilpotent induced connections induced the connection of Grifone, Connections in a Riemannian manifold , Grifone’s connection.