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MATH 662 —
Spring 2000
Riemannian Geometry
| Instructor: |
José F. Escobar |
| Time: |
MWF 10:10-11:00 |
| Room: |
MT 205 |
I will cover the following topics: Linear connections, Riemannian metrics
and parallel translation. Covariant differentiation and curvature tensors.
The exponential map, the Gauss Lemma and completeness of the metric. Isometries
and space forms. Jacobi fields and the theorem of Cartan-Hadamard. The
first and second variation formulas. The index form of Morse and the theorem
of Bonnet-Myers. The Rauch, Hessian, and Laplacian comparison theorems.
The Morse index theorem. The conjugate and cut loci. Submanifolds and
the Second Fundamental form.
Last modified:
April 7, 2003
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