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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: Mo 07.09.2020 15:40