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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.
TypeLecture
InstructorProf. Dr. Konrad Polthier
LanguageEnglish
Credit Points10
RoomArnimallee 6
StartOct 19, 2021 | 12:15 PM
endFeb 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: March, 3rd, 2022, 10-12, and retake: March, 31st, 2022, more details will be displayed during the term.

Note

*The lecture on DECEMBER, 2ND, is cancelled.

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