Universität Wien

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