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# Differential Geometry I

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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 Prof. Dr. Konrad Polthier English 10 Arnimallee 6 Oct 19, 2021 | 12:15 PM 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').

## 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