MTH-211.4 Smooth Manifolds and Riemannian Geometry
Syllabus
Part A: Smooth Manifolds
1. Definition of smooth manifolds and properties
2. Smooth maps between manifolds
3. Tangent and cotangent bundle
4. Submersion, immersion and smooth embeddings
5. Embedded and immersed submanifolds
6. Introduction to tensor algebra and differential forms
7. Integration on Manifolds
Part B: Riemannian Geometry
1. Riemannian metrics, some model examples
2. Levi Civita Connection
3. Geodesics and distance
4. Introduction to curvature
5. Riemannian submanifolds
6. Jacobi Fields