Universität Wien
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250077 VO Selected topics in differential geometry (2009W)

5.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 06.10. 17:00 - 18:40 Seminarraum
  • Thursday 08.10. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 13.10. 17:00 - 18:40 Seminarraum
  • Thursday 15.10. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 20.10. 17:00 - 18:40 Seminarraum
  • Thursday 22.10. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 27.10. 17:00 - 18:40 Seminarraum
  • Thursday 29.10. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 03.11. 17:00 - 18:40 Seminarraum
  • Thursday 05.11. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 10.11. 17:00 - 18:40 Seminarraum
  • Thursday 12.11. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 17.11. 17:00 - 18:40 Seminarraum
  • Thursday 19.11. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 24.11. 17:00 - 18:40 Seminarraum
  • Thursday 26.11. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 01.12. 17:00 - 18:40 Seminarraum
  • Thursday 03.12. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Thursday 10.12. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 15.12. 17:00 - 18:40 Seminarraum
  • Thursday 17.12. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Thursday 07.01. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 12.01. 17:00 - 18:40 Seminarraum
  • Thursday 14.01. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 19.01. 17:00 - 18:40 Seminarraum
  • Thursday 21.01. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II
  • Tuesday 26.01. 17:00 - 18:40 Seminarraum
  • Thursday 28.01. 17:00 - 18:40 Seminarraum 2A310 3.OG UZA II

Information

Aims, contents and method of the course

*) Focal points
*) Variation of energy
*) Focal points along null geodesics
*) Causality
*) Convex coverings
*) Quasi-limits
*) Causality conditions
*) Time separation
*) Globally hyperbolic sets
*) Achronal sets
*) Cauchy hypersurfaces
*) Cauchy developments
*) Cauchy horizons
*) Singularity theorems

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

Based on the course "Global semi-Riemannian Geometry", in this lecture course we give a complete proof of the singularity theorems of Hawking and Penrose. The necessary prerequisites from calculus of variations and causality in Lorentz manifolds will be developed in the course.

Examination topics

Reading list

C. Bär, Lorentzgeometrie, Vorlesungsskriptum
S.W. Hawking, G.F.R. Ellis, The large scale structure of space-time
B. O'Neill, Semi-Riemannian Geometry

Association in the course directory

MGEV

Last modified: Sa 02.04.2022 00:24