Mondays, Wednesdays 2:50-4:05, Physics 205
This course is a graduate-level introduction to foundational material in differential geometry. Differential geometry underlies modern treatments of many areas of mathematics and physics, including geometric analysis, topology, gauge theory, general relativity, and string theory. The main topics of study will be: differential manifolds, vector fields, tensors, differential forms, and vector bundles; Riemannian metrics, connections, geodesics, curvature, and topological curvature theorems. Additional advanced topics will be considered if time permits.
The textbook for this course is Riemannian Geometry by Manfredo Perdigão do Carmo. As a supplementary source, some of the material covered in the class can be found in Riemannian Geometry by Gallot, Hulin, and Lafontaine.