Universität Wien

250070 VO Riemannian geometry (2021W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
MIXED
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 05.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.10. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.11. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.12. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.12. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.01. 09:45 - 11:15 Seminarraum 10 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course is part of the core modules for the area of specialization "geometry and topology" in the master program, it can be used as an elective in all other areas. Building on a good background on analysis on manifolds, we will develop the fundamentals of Riemannian geometry.

Contents: Riemannian metrics and Riemannian manifolds; covariant derivative and parallel transport; geodesics, exponential mapping and normal coordinates; Riemann curvature tensor, derived curvature quantities and their geometric interpretation; special classes of Riemannian manifolds;

The current plan is to teach the course in presence. To be on the safe side, there will be a moodle page for the course which will be the main point of contact for the course, in particular if distance teaching becomes neccessary.

Assessment and permitted materials

oral exam after the end of the course

Minimum requirements and assessment criteria

Students know the fundamental concepts and results of Riemannian geometry as discussed in the course and can describe the proofs of the central results in the area; the usual standards for lecture courses in the master program are employed

Examination topics

the contents of the course

Reading list

Lecture notes for the course will be distributed via the webpage https://www.mat.univie.ac.at/~cap/lectnotes.html in due time. (The version from 2014/15 that is currently online there will be reworked soon.)

There is a large supply of introductory books on Riemannian geometry. Books that work in the setting of abstract Riemannian manifolds (rather than just on submanifolds of Euclidean space) will in general cover (almost) all the material discussed in the course. Choosing between the available books then rather is a matter of taste.

Association in the course directory

MGED

Last modified: Fr 03.11.2023 00:20