VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

401-3531-00L 10 Credits
You're viewing possible stale or outdated data. Please check the latest semester for more up-to-date information.

Differential Geometry

Differentialgeometrie I

Lecturers & Examiners: Prof. Dr. Tom Ilmanen
VVZ CR n/a

Last Updated: 2026-02-05 14:59:48

Abstract

Manifolds, submanifolds, immersions, submersions and diffeomorphisms, tangent bundle, vector bundles, Whitney sum, smooth partitions of unity, Riemannian manifolds, geodesics, Levi-Civita connection, covariant derivatives, theorem of Hopf-Rinow, submanifolds of Riemannian manifolds, first and second fundamental form, curvature

Content

Mannigfaltigkeiten, Untermannigfaltigkeiten, Immersionen, Submersionen und Diffeomorphismen, Tangentialbündel und Vektorbündel, Whitneysumme von Vektorbündeln, Glatte Partitionen der Eins, Riemannsche Mannigfaltigkeiten, Geodäten, Levi-Civita Zusammenhang, kovariante Ableitungen, Hopf-Rinow Theorem, Untermannigfaltigkeiten Riemannscher Mannigfaltigkeiten, erste und zweite Fundamentalform, Krümmungsbegriffe.

General Information

Language
English (lecture), German (exercise)
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 D 3.2)
  • Fri 10:15-12:00 (HG G 5)
4 h weekly
exercise Differentialgeometrie I
Fr 9-10 für Studiengang Physik
  • Mon 11:15-12:00 (NO C 4)
  • Mon 11:15-13:00 (HG G 26.1)
  • Fri 08:15-09:00 (HG F 26.3)
  • Fri 09:15-10:00 (HG F 26.3)
  • Fri 13:15-15:00 (HG D 5.2)
  • Fri 13:15-15:00 (HG F 26.5)
1 h weekly

Offered In