MA 333: Riemannian Geometry
Credits: 3:0
Riemannian metric, Levi-Civita connection, geodesics, exponential map, Hopf-Rinow theorem, curvature tensior, first and second variational formula, jacobi fields, Myers Bonnet theorem, Bishop-Gromov volume comparison theorem, Cartan-Hadamard theorem, Synge’s theorem, de Rham cohomology and the Bochner techniques. Topological implications of positive or negative curvature.
Suggested books and references:
- Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine, Riemannian geometry, Third edition. ,Universitext. Springer-Verlag, Berlin, 2004.
- Peter Petersen, Riemannian geometry ,Graduate Texts in Mathematics, 171. Springer-Verlag, New York, 1998.