Differential Geometry I
(19202601)
Regular participation: at least 85% of participation in the tutorials is needed. Active participation: at least 60% of all possible points that can be earned in the homework assignments are needed.| Type | Lecture |
|---|---|
| Instructor | Prof. Dr. Konrad Polthier |
| Language | English |
| Credit Points | 10 |
| Room | Arnimallee 6 |
| Start | Oct 19, 2021 | 12:15 PM |
| end | Feb 17, 2022 | 02:00 PM |
| Time | *Lecture: Tuesday, 12:00 - 14:00, via WebEx, Thursday, 12:00 - 14:00, via WebEx *Tutorials: Friday, 08:00 - 10:00, via WebEx *Written Exams (online): March, 3rd, 2022, 10-12, and retake: March, 31st, 2022, 10-12. |
| Note | Information on the processing of the exams can be found below under "Downloads" (see 'Information Exam Processing' and 'GEE'). |
Requirements
Analysis I-II,
Linear Algebra I-II
Literature
- W. Kühnel: Differentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012 (english edition: Differential Geometry: Curves - Surfaces - Manifolds, Springer)
- M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
- J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
- C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001 (english edition: Elementary Differential Geometry, de Gruyter)
- M. Spivak: A Comprehensive Introduction To Differential Geometry, Publish or Perish, 1999
Differential geometry studies local and global properties of curved spaces.
Topics of the lecture will be:
- Curves and surfaces in Euclidean space
- Metrics and (Riemannian) manifolds
- Surface tension and notions of curvature
- Vector fields, tensors, covariant derivative
- Geodesic curves, exponential map
- Gauß-Bonnet theorem, curvature and topology
- Connection to discrete differential geometry
Prerequisits: Analysis I, II and Linear Algebra I, II