250017 VO Differential geometry 2 (2010W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

Details

Language: German

Examination dates

Lecturers

Stefan Haller

Classes (iCal) - next class is marked with N

Monday 04.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 05.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 07.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 11.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 12.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 14.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 18.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 19.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 21.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 25.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 28.10. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 04.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 08.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 09.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 11.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 15.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 16.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 18.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 22.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 23.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 25.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 29.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 30.11. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 02.12. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 06.12. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 07.12. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 09.12. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 13.12. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 14.12. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 16.12. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 10.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 11.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 13.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 17.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 18.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 20.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 24.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Tuesday 25.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Thursday 27.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II
Monday 31.01. 12:05 - 12:50 Seminarraum 2A310 3.OG UZA II

Information

Aims, contents and method of the course

Among other things we will discuss the following topics: DeRham cohomology and Poincaré duality, vector bundles, linear connections and covariant derivative, parallel transport, curvature, (pseudo-)Riemannian manifolds, Levi-Civita connection, geodesics and exponential mapping, theorem of Hopf-Rinow, symplectic geometry.

For further information see: http://www.mat.univie.ac.at/~stefan/DGII2010.html

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

Basic knowledge on differential geometry.

Examination topics

Reading list

A. Cap, Differentialgeometrie I, Vorlesungsskriptum 2004. http://www.mat.univie.ac.at/~cap/files/diffgeom.pdf

A. Kriegl, Differentialgeometrie, Vorlesungsskriptum 2009. http://www.mat.univie.ac.at/~kriegl/Skripten/2009SS.pdf

K. Jänich, Vektoranalysis, Springer-Verlag, Berlin.

P.W. Michor, Topics in differential geometry, Graduate Studies in Mathematics 93, AMS Providence, RI, 2008.

J. Jost, Riemannian geometry and geometric analysis, Universitext, Springer-Verlag, Berlin.

W. Klingenberg, Riemannian geometry, de Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin.

R. Bott and L.W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics 82, Springer-Verlag, New York-Berlin.

Association in the course directory

MGED

Last modified: Sa 02.04.2022 00:24