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401-3532-08L 9 Credits BSC , MSC D-PHYS , D-MATH
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Differential Geometry II

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

Last Updated: 2026-06-01 11:33:37

Abstract

Introduction to Riemannian geometry in combination with some elements of modern metric geometry. Contents: Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, relations between curvature and topology, spaces of Riemannian manifolds.

Objective

Learn the basics of Riemannian geometry and some elements of modern metric geometry.

Resources

Literature

- M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992 - S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004 - B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press 1983 - S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Volume I, Wiley 1963

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Differential Geometry II
  • Mon 14:15-16:00 (HG G 5)
  • Thu 10:15-12:00 (CAB G 11)
4 h weekly
exercise Differential Geometry II
Groups are selected in myStudies. Fri 10-11
  • Fri 10:15-11:00 (HG D 5.2)
  • Fri 11:15-12:00 (HG D 5.2)
1 h weekly

Offered In