Instructor: | Ibrahim Unal |
Classes: | Mon. 11:40-12:30, Wed. 10:40-12:30 (M-215) |
Office-Hours: | Thur. 08:40-10:30 in M-241 |
Textbook: | John M. Lee, Intro. to Riemannian Manifolds, 2. Ed. |
Aux. Textbook: | Peter Petersen, Riemannian Geometry, 3. Ed. |
Review of curvature tensor, sectional curvature. Ricci tensor, scalar curvature. Riemannian submanifolds. Gauss and Codazzi equations. Lie groups. Symmetric spaces. Principle fibre bundles. Almost complex and complex manifolds; Hermitian and Kaehlerian geometry.
Week | Topic | Assignment |
---|---|---|
1 | Review of Curvature Tensor, Sectional curvature. Ricci tensor, Scalar Curvature. | |
2 | Model Riemannian Manifolds | |
3 | Model Riemannian Manifolds | |
4 | Jacobi Fields | |
5 | Second Variational Formula | |
6 | Riemannian Submanifolds | |
7 | Gauss and Codazzi Equations | |
8 | Lie Groups | |
9 | Metrics on Lie Groups | |
10 | Symmetric Spaces | |
11 | Symmetric Spaces | |
12 | Complex Manifolds | |
13 | Hermitian and Kahler Geometry | |
14 | Fibre Bundles | |
15 | Final Exam |
Homeworks | 30% | ||
Midterm | 30% | ||
Final | 40% |
● M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. I, II
● J. Jost, Riemannian Geometry and Geometric Analysis