Universität Wien
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250070 VO Riemannian geometry (2019W)

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

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

This course is blocked into the first half of the semester. The last lecture will be on Thursday, November 28.

  • Monday 07.10. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.10. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.10. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.10. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.10. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.10. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.10. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.10. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.11. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.11. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.11. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.11. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.11. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.11. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 25.11. 16:45 - 18:15 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.11. 17:00 - 18:30 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The course "Analysis on Manifolds" (as taught by Michael Eichmair in the summer term 2020 or equivalent knowledge) is a prerequisite for this class.

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)

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

Assessment and permitted materials

thorough half-hour oral exam

Minimum requirements and assessment criteria

Examination topics

Everything that is covered in class.

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 2019. 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: Tu 20.10.2020 14:09