RIEMANNIAN GEOMETRY
Prerequisites: MA 331 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.
Books
* 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.
Timings !0. 30 to 12 Noon on Tuesdays & Thursdays at Lecture Hall - II