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Riemannian and Sub-Riemannian geometry Description

Key Elements

Code

MATH 500

Formation

M2 Differential Geometry

Semester

1

Credits

4

Number of Teaching Hours

48

Number of Tutoring Sessions

0

Number of Laboratory Sessions

0

Content

Objective

Content

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.