This class is an introduction to Riemannian geometry.
In particular, we will study various notions of curvature and their relations with the global structure or topology of a manifold.

Prerequisites

Math 6458 or some familiarity with basic theory of differential manifolds.

Textbooks

Instructor's notes and Riemannian Geometry by Manfredo Do Carmo.

Grading

The grade is based on class participation (the students are expected to attend all lectures) and homework assignments.