Differential Geometry I

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 and covariant derivative,
* geodesic curves and the exponential map,
* Gauß-Bonnet theorem and topology,
* discrete differential geometry.

(19202601)

participation in the tutorials: at least 85 % are required amount of points in the homeworks: at least 60 % are required

Type

Lecture

Instructor

Prof. Dr. Konrad Polthier

Language

English

Room

Arnimallee 6

Time

* Lecture: Monday, 12 -14, SR 031/A7 (starting Oct., 16th, 2017)

               Wednesday, 12-14, SR 007/008/A6

* Tutorials (starting Oct., 19th, 2017):  

* A: Thursday, 10-12, 046/T9 (english)

* B: Friday, 10-12, 009/A6 (german)

*Exams:

* February, 21st, 2018, 10 - 12 am, Hörsaal 001/A3
* April, 9th, 2018, 10 - 12 am, Hörsaal 001/A3

Start

Oct 16, 2017 | 12:00 PM — Feb 16, 2018 | 06:00 PM

Note

Happy new year - there were two phis lost in the additional exercise of sheet 8. Corrected version is uploaded.

Requirements

Analysis I-III,

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
  • Ch. Bär: Elementare Differentialgeometrie, de Gruyter, 2001 (english edition: Elementary Differential Geometry, de Gruyter)
  • M. Spivac: A Comprehensive Introduction To Differential Geometry, Publish or Perish, 1999