250070 VO Riemannian Geometry (2023W)
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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
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.
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: Fr 08.03.2024 11:26
- 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.