Géométrie Riemannienne

MATH 4203: Riemannian geometry

Prerequisites: the course of advanced geometry of the 1st semester

Program:

- Vector bundles

- Introduction to Riemannian geometry:

Riemannian metrics, Riemannian volume form, Divergence of a vector field, Riemannian gradient of a function, Laplace-Beltrami operator, Harmonic functions, Conformal diffeomorphisms, Existence of isothermal coordinates on Riemannian surfaces,

- Connections

- Geodesics, and their variational theory

- Curvature of Riemannian manifolds

- Gauss' Theorema Egregium

- Gauss-Bonnet's Theorem

- A few results concerning conjugate points