| When taught: | Fall, every year |
| Suggested text ($): | M. do Carmo, Riemannian Geometry ISBN-10: 0817634908 ($55) |
| Units/lectures: | 4 units; lecture/term paper or discussion |
| Prerequisite: | Course 201A and 239; 250AB highly recommended; intended primarily for 2nd-year graduate students. |
Riemannian metrics, connections, geodesics, Gauss lemma, convex neighborhoods, curvature tensor, Ricci and scalar curvature, connections and curvature on vector bundles.
| Prepared in 2008 by: | Michael Kapovich |
| Posted: | July 2009 |
| Lectures | Sections | Topics/Comments |
|---|---|---|
| First 4 chapters of do Carmo's book | Riemannian metrics, connections, geodesics, Gauss lemma, convex neighborhoods, curvature tensor, Ricci and scalar curvature. | |
| Examples of Riemannian metrics and computation of connection and curvature: sphere, compact Lie groups, hyperbolic space. | ||
| Also cover: connections and curvature on vector bundles using, for instance, Kobayashi and Nomizu. | ||
| Supplementary topics: G-structures, pseudo-Riemannian metrics, Einstein metrics, holonomy. | ||
| Supplementary Reading | P. Petersen, Riemannian Geometry J. Jost, Riemannian Geometry and Geometric Analysis S. Kobayashi, Transformation Groups in Differential Geometry. Classics in Mathematics S. Kobayashi and K. Nomizu, Foundations of Differential Geometry |