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Differential Geometry I
Differentialgeometrie I
Last Updated: 2026-02-05 15:14:49
Abstract
Curves in R^n, inner geometry of hypersurfaces in R^n, Gauss map and curvature, Theorema Egregium, minimal surfaces, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, tangent bundle, immersions and embeddings, Sard's theorem, transversality, degree and intersection number.
Objective
Introduction to elementary differential geometry and differential topology.
Content
- Differential geometry in R^n: theory of curves, submanifolds and immersions, tangent space, inner geometry of hypersurfaces, Gauss map and curvature, Theorema Egregium, minimal surfaces, Theorem of Gauss-Bonnet. - The hyperbolic space. - Differential topology: differentiable manifolds, tangent bundle, immersions and embeddings in R^n, Sard's theorem, transversality, degree and intersection number.
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 I |
|
4 h weekly |
| exercise | Differentialgeometrie I |
|
1 h weekly |