Universität Wien

250070 VO Riemannian geometry (2019W)

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

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

thorough half-hour oral exam

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

Everything that is covered in class.

Literatur

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.

Zuordnung im Vorlesungsverzeichnis

MGED

Letzte Änderung: Di 20.10.2020 14:09