M39: Topics in Riemannian Geometry

This course can be seen as a "second" course in Riemannian geometry. The target audience is advanced Bachelors's and Masters's studentsand PhD students and basic knowledge of Riemannian geometry and computations involving tensor calculus will be assumed. A (preliminary) discussion of topics is outlined below.

Topics to be covered:

1. Basics of Riemannian geometry and Ricci calculus with emphasis on calculations in local coordinates. Curvature-type tensors.>
2. Compraison theorems in Riemannian geometry.
3. The Bochner technique and its applications.