Universität Wien
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250076 VO Differential geometry 2 (2012W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 02.10. 14:05 - 14:55 Seminarraum
  • Wednesday 03.10. 12:05 - 12:55 Seminarraum
  • Thursday 04.10. 13:05 - 13:55 Seminarraum
  • Tuesday 09.10. 14:05 - 14:55 Seminarraum
  • Wednesday 10.10. 12:05 - 12:55 Seminarraum
  • Thursday 11.10. 13:05 - 13:55 Seminarraum
  • Tuesday 16.10. 14:05 - 14:55 Seminarraum
  • Wednesday 17.10. 12:05 - 12:55 Seminarraum
  • Thursday 18.10. 13:05 - 13:55 Seminarraum
  • Tuesday 23.10. 14:05 - 14:55 Seminarraum
  • Wednesday 24.10. 12:05 - 12:55 Seminarraum
  • Thursday 25.10. 13:05 - 13:55 Seminarraum
  • Tuesday 30.10. 14:05 - 14:55 Seminarraum
  • Wednesday 31.10. 12:05 - 12:55 Seminarraum
  • Tuesday 06.11. 14:05 - 14:55 Seminarraum
  • Wednesday 07.11. 12:05 - 12:55 Seminarraum
  • Thursday 08.11. 13:05 - 13:55 Seminarraum
  • Tuesday 13.11. 14:05 - 14:55 Seminarraum
  • Wednesday 14.11. 12:05 - 12:55 Seminarraum
  • Thursday 15.11. 13:05 - 13:55 Seminarraum
  • Tuesday 20.11. 14:05 - 14:55 Seminarraum
  • Wednesday 21.11. 12:05 - 12:55 Seminarraum
  • Thursday 22.11. 13:05 - 13:55 Seminarraum
  • Tuesday 27.11. 14:05 - 14:55 Seminarraum
  • Wednesday 28.11. 12:05 - 12:55 Seminarraum
  • Thursday 29.11. 13:05 - 13:55 Seminarraum
  • Tuesday 04.12. 14:05 - 14:55 Seminarraum
  • Wednesday 05.12. 12:05 - 12:55 Seminarraum
  • Thursday 06.12. 13:05 - 13:55 Seminarraum
  • Tuesday 11.12. 14:05 - 14:55 Seminarraum
  • Wednesday 12.12. 12:05 - 12:55 Seminarraum
  • Thursday 13.12. 13:05 - 13:55 Seminarraum
  • Tuesday 18.12. 14:05 - 14:55 Seminarraum
  • Tuesday 08.01. 14:05 - 14:55 Seminarraum
  • Wednesday 09.01. 12:05 - 12:55 Seminarraum
  • Thursday 10.01. 13:05 - 13:55 Seminarraum
  • Tuesday 15.01. 14:05 - 14:55 Seminarraum
  • Wednesday 16.01. 12:05 - 12:55 Seminarraum
  • Thursday 17.01. 13:05 - 13:55 Seminarraum
  • Tuesday 22.01. 14:05 - 14:55 Seminarraum
  • Wednesday 23.01. 12:05 - 12:55 Seminarraum
  • Thursday 24.01. 13:05 - 13:55 Seminarraum
  • Tuesday 29.01. 14:05 - 14:55 Seminarraum
  • Wednesday 30.01. 12:05 - 12:55 Seminarraum
  • Thursday 31.01. 13:05 - 13:55 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: Sa 17.04.2021 00:29