Universität Wien

250070 VO Riemannian Geometry (2023W)

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

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 04.10. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.10. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.10. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.10. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.10. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.10. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.10. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.11. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.12. 16:45 - 18:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

We will cover the following topics:

- Local Riemannian Geometry (including a proof that short geodesics are minimizing)
- Abstract Riemannian Manifolds (including the Levi-Civita connection and curvature)
- Geodesics (including first and second variation of length, Jacobi fields, completeness)
- Applications (including Hopf-Rinow, Bonnet-Myers, Gauss-Bonnet, azimuthal coordinates)
- Elements of comparison geometry (Rauch comparison theorem, Bishop-Gromov volume comparison theorem)

We will likely cover additional topics, taking the interests of the audience into account.

Assessment and permitted materials

There will be a thorough half hour oral exam.

Minimum requirements and assessment criteria

Examination topics

All material covered in class is examinable.

Reading list

Lecture notes will be provided for large portions of the class.
I recommend the books by do Carmo (Riemannian Geometry), O'Neill (Semi-Riemannian Geometry), and by Petersen (Riemannian Geometry) for supplementary reading. They differ greatly in style and emphasis. For the exam, I ask that you are familiar with the notation and the proofs as given in class and the lecture notes.
The prerequisites are covered well by the lecture notes for »Analysis on Manifolds« as taught in the summer term of 2023. The moodle platform is still active and can be accessed using the same password as for this course.

Association in the course directory

MGED

Last modified: Th 26.09.2024 15:46