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.
|Instructor||Prof. Dr. Konrad Polthier|
|Start||Oct 19, 2021 | 12:15 PM|
|end||Feb 17, 2022 | 02:00 PM|
*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.
Information on the processing of the exams can be found below under "Downloads" (see 'Information Exam Processing' and 'GEE').
Linear Algebra I-II
- 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