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Differential Geometry I
| Time and room: | |||
| Professor |
Prof. Dr. Rahul Pandharipande |
|
We 08-10, HG G 3 |
| Fr 10-12, HG F 3 | |||
| Coordinator |
Roger Züst |
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|
Surname |
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Assistants |
Martin Sack |
A-Ga | We 15-16, HG G 26.1 |
|
Tobias Strubel |
Ge-Lei |
We 15-16, HG G 3 | |
|
Bledar Fazlija |
Leo-Re |
We 15-16, CAB G 57 | |
|
Christian Graf |
Ro-Z |
Fr 09-10, HG G 26.1 |
| Syllabus |
|
Differentiable manifolds, tangent bundle, embeddings, Frobenius' theorem. Geodesics, second fundamental form, completeness, Hopf-Rinow theorem. Levi-Civita connection, parallel transport, Christoffel symbols, frame bundle. Isometries, Riemann curvature tensor, Bianchi identities, Teorema Egregium, Cartan-Ambrose-Hicks theorem, constant curvature, symmetric spaces. |
| References |
|
1. Riemannian Geometry, M.P. do Carmo.
2. Foundations of Differentiable Manifolds and Lie Groups, F.W. Warner. The exact sections out of the books above that have been covered in the course and some sample questions for the oral exam can be found here: |
| The course starts: We 21. September 2011. |
| The exercises start: We 28. September and Fr 30. September. |
| Exercises: The details are here. |
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