This class is an introduction to Riemannian geometry.
In particular, we will study geodesics, the Riemann curvature tensor, Jacobi fields, Hopf-Rinow and Hadamard theorems, and spaces of constant curvature.

Prerequisites

Math 6457 or Math 4441.

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.