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401-3531-00L 10 Credits BSC , MSC D-PHYS , D-MATH
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Differential Geometry I

Differentialgeometrie I

Lecturers & Examiners: Prof. Dr. Urs Lang
VVZ CR n/a

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
  • Wed 13:15-15:00 (HG G 3)
  • Fri 10:15-12:00 (HG G 5)
4 h weekly
exercise Differentialgeometrie I
  • Mon 11:15-12:00 (HG E 21)
  • Fri 09:15-10:00 (HG F 26.3)
  • Fri 09:15-10:00 (HG G 26.3)
  • Fri 13:15-15:00 (HG F 26.5)
1 h weekly

Offered In