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:

  1. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine, Riemannian geometry, Third edition. ,Universitext. Springer-Verlag, Berlin, 2004.
  2. Peter Petersen, Riemannian geometry ,Graduate Texts in Mathematics, 171. Springer-Verlag, New York, 1998.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 09 Apr 2019