MATH 546: Differential Geometry II

Spring 2022

Textbook

Course information

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.

Course Content

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.

Tentative Weekly Outline

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

Grading

Homeworks   30%
Midterm   30%  
Final   40%  

Homeworks

References