Universität Wien
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250060 VO Differential geometry 2 (2008W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 06.10. 13:15 - 14:45 Seminarraum
  • Tuesday 07.10. 13:15 - 14:00 Seminarraum
  • Monday 13.10. 13:15 - 14:45 Seminarraum
  • Tuesday 14.10. 13:15 - 14:00 Seminarraum
  • Monday 20.10. 13:15 - 14:45 Seminarraum
  • Tuesday 21.10. 13:15 - 14:00 Seminarraum
  • Monday 27.10. 13:15 - 14:45 Seminarraum
  • Tuesday 28.10. 13:15 - 14:00 Seminarraum
  • Monday 03.11. 13:15 - 14:45 Seminarraum
  • Tuesday 04.11. 13:15 - 14:00 Seminarraum
  • Monday 10.11. 13:15 - 14:45 Seminarraum
  • Tuesday 11.11. 13:15 - 14:00 Seminarraum
  • Monday 17.11. 13:15 - 14:45 Seminarraum
  • Tuesday 18.11. 13:15 - 14:00 Seminarraum
  • Monday 24.11. 13:15 - 14:45 Seminarraum
  • Tuesday 25.11. 13:15 - 14:00 Seminarraum
  • Monday 01.12. 13:15 - 14:45 Seminarraum
  • Tuesday 02.12. 13:15 - 14:00 Seminarraum
  • Tuesday 09.12. 13:15 - 14:00 Seminarraum
  • Monday 15.12. 13:15 - 14:45 Seminarraum
  • Tuesday 16.12. 13:15 - 14:00 Seminarraum
  • Monday 12.01. 13:15 - 14:45 Seminarraum
  • Tuesday 13.01. 13:15 - 14:00 Seminarraum
  • Monday 19.01. 13:15 - 14:45 Seminarraum
  • Tuesday 20.01. 13:15 - 14:00 Seminarraum
  • Monday 26.01. 13:15 - 14:45 Seminarraum
  • Tuesday 27.01. 13:15 - 14:00 Seminarraum

Information

Aims, contents and method of the course

This lecture provides an introduction to semi-Riemannian (in particular: Riemannian and Lorentzian) geometry. The following topics will be discussed:

* Manifolds and tensors
o submanifolds
o Vector fields and flows
o Tensors
o Scalar products
* Semi-Riemannian Manifolds
o Semi-Riemannian metrics
o The Levi-Civita connection
o Geodesics and exponential map
o Geodesic convexity
o Bogenlänge und Riemannsche Distanz
o The Hopf-Rinow theorem
o Curvature
o Metric contraction
o Local frames
o Differential operators
o The Einstein equations
o Semi-Riemannian submanifolds

Assessment and permitted materials

Oral Exam

Minimum requirements and assessment criteria

This lecture course aims at providing a solid foundation both for a further study of Riemannian geometry and for applications, in particular in general relativity.

Examination topics

Reading list

F. Brickel, R.S. Clark, Differentiable Manifolds. An Introduction.
W. M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry.
M. do Carmo, Riemannian Geometry.
S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry.
A. Kriegl, Differentialgeometrie (Skriptum, http://www.mat.univie.ac.at/~kriegl/Skripten/diffgeom.pdf ).
W. Kühnel, Differentialgeometrie. Kurven - Flächen - Mannigfaltigkeiten.
M. Kunzinger, Differential Geometry 1 (Skriptum, http://www.mat.univie.ac.at/~mike/teaching/ss08/dg.pdf)
B. O'Neill, Semi-Riemannian manifolds. With applications to relativity.

Association in the course directory

MGED

Last modified: Mo 07.09.2020 15:40