Details of MA5114 (Autumn 2024)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5114 | Riemannian Geometry | Arjun Paul |
| Syllabus |
|---|
| Metric: Definition of Riemannian metric and Riemannian manifolds.
Connections: Definition, Levi-Civita connection, covariant derivatives, parallel transport. Geodesics: The concepts of geodesics, geodesics in the upper half plane, first variational formula, local existence and uniqueness of geodesics, the exponential map, Hopf-Rinow theorem. Curvature: Curvature tensor and fundamental form, computation of curvature with examples, Ricci, sectional and scalar curvature. |
| Prerequisite |
|---|
| Differential Geometry (MA4205)
|
| References |
|---|
| Suggested Texts:
1. Do Carmo, M., Riemannian Geometry, Birkhauser. 2. Gallot, S., Hulin, D. and Lafontaine, J., Riemannian Geometry, Springer. 3. Helgason, S., Differential Geometry, Lie Groups and Symmetric Spaces, American Mathematical Society. 4. Lee, J., Riemannian Manifolds, Springer. 5. Milnor, J.W., Morse Theory, Hindustan Book Agency. 6. Spivak M., A comprehensive Introduction to Differential Geometry, Vols. I & II, 3rd Edition, Publish or Perish. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MP | 1 | Not Allowed |
| 5 | MP | 3 | Not Allowed |
| 6 | MR | 1 | Not Allowed |
| 7 | MR | 3 | Not Allowed |
| 8 | MS | 3 | Not Allowed |
| 9 | MS | 5 | Not Allowed |
| 10 | MS | 7 | Not Allowed |
| 11 | MS | 9 | Elective |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |