Universität Wien
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250070 VO Selected topics in differential geometry: Global semi-Riemannian geometry (2009S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 03.03. 17:10 - 18:50 Seminarraum
  • Thursday 05.03. 17:10 - 18:50 Seminarraum
  • Tuesday 10.03. 17:10 - 18:50 Seminarraum
  • Tuesday 17.03. 17:10 - 18:50 Seminarraum
  • Thursday 19.03. 17:10 - 18:50 Seminarraum
  • Tuesday 24.03. 17:10 - 18:50 Seminarraum
  • Thursday 26.03. 17:10 - 18:50 Seminarraum
  • Tuesday 31.03. 17:10 - 18:50 Seminarraum
  • Thursday 02.04. 17:10 - 18:50 Seminarraum
  • Tuesday 21.04. 17:10 - 18:50 Seminarraum
  • Thursday 23.04. 17:10 - 18:50 Seminarraum
  • Tuesday 28.04. 17:10 - 18:50 Seminarraum
  • Thursday 30.04. 17:10 - 18:50 Seminarraum
  • Tuesday 05.05. 17:10 - 18:50 Seminarraum
  • Thursday 07.05. 17:10 - 18:50 Seminarraum
  • Tuesday 12.05. 17:10 - 18:50 Seminarraum
  • Thursday 14.05. 17:10 - 18:50 Seminarraum
  • Tuesday 19.05. 17:10 - 18:50 Seminarraum
  • Tuesday 26.05. 17:10 - 18:50 Seminarraum
  • Thursday 28.05. 17:10 - 18:50 Seminarraum
  • Thursday 04.06. 17:10 - 18:50 Seminarraum
  • Tuesday 09.06. 17:10 - 18:50 Seminarraum
  • Tuesday 16.06. 17:10 - 18:50 Seminarraum
  • Thursday 18.06. 17:10 - 18:50 Seminarraum
  • Tuesday 23.06. 17:10 - 18:50 Seminarraum
  • Thursday 25.06. 17:10 - 18:50 Seminarraum
  • Tuesday 30.06. 17:10 - 18:50 Seminarraum

Information

Aims, contents and method of the course

1. Semi-Riemannian submanifolds
Induced connection, shape operator, curvature, local isometries, totally geodesic submanifolds, semi-Riemannian hypersurfaces, hyperquadrics, Codazzi equation, normal connection.
2. Lorentz Geometry
Causal character, timecones, local Lorentz geometry.
3. Calculus of Variations
First and second variation, Jacobi fields, index form, conjugate points, local maxima and minima, global structure of semi-Riemannian manifolds, endmanifolds, normal bundle, focal points, energy, causality.

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

Building on basic knowledge of (semi-)Riemannian geometry, this course intends to provide a deeper understanding, particularly of the global aspects of the subject. We will focus on topics that are relevant for applications in general relativity.

Examination topics

Reading list

B. O'Neill, Semi-Riemannian Geometry

Association in the course directory

MGEV

Last modified: Mo 07.09.2020 15:40