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Differential Geometry II
Differentialgeometrie II
Last Updated: 2026-02-05 15:29:41
Abstract
Continuation of Differential Geometry I. Vector bundles, vector fields and flows.Differential forms, Theorem of Stokes, de Rham cohomology. Introduction to Lie groups. Riemannian manifolds, Theorem of Hopf-Rinow, curvature, Theorems of Synge and Bonnet-Myers, Rauch Comparison Theorem, Theorem of Hadamard-Cartan, space forms.
Objective
Introduction to Riemannian Geometry.
Content
- Vector bundles, vector fields and flows, Lie bracket. - Differential forms, integration, Theorem of Stokes, de Rham cohomology. - Introduction to Lie groups. - Riemannian manifolds, Levi-Civita connection, exponential map, Theorem of Hopf-Rinow. - Riemannian curvature tensor, sectional, Ricci, and scalar curvature. - Second variation of arc-length, Jacobi fields and conjugate points, Theorems of Synge and Bonnet-Myers, index form, Rauch Comparison Theorem. - Riemannian submersions and coverings, Theorem of Hadamard-Cartan, space forms, growth of the fundamental group.
General Information
- Language
- German
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Differentialgeometrie II |
|
4 h weekly |
| exercise | Differentialgeometrie II |
|
1 h weekly |