Math 226A: Differential Geometry

Fall 2013

Riemannian geometry is the study of smooth manifolds equipped with Riemannian metrics. It is the language of Einstein's theory of general relativity, and of many of the modern developments in physics, such as gauge theory and string theory. It has also had an impact on numerous areas of mathematics, from analysis to algebraic geometry. The Ricci flow, a concept coming from differential geometry, was recently used by Perelman to prove the Poincare Conjecture.

In this course we will cover the following topics:

Prerequisite: A working knowledge of smooth manifolds, differential forms and de Rham cohomology, at the level of Math 225A and Math 225B.

Grading: Based on a few problem sets.

Textbook: P. Petersen, Riemannian Geometry, 2nd edition, Springer Verlag, 2006.

Other recommended books:

Problem sets: