Differential Geometry I

Differential geometry studies the local and global properties of curved spaces.

Topics of the lecture will be:

* curves and surfaces in Euclidean space,
* (Riemannian) manifolds,
* vector bundles, especially the tangent bundle,
* tensors,
* curvature tensors,
* submanifolds,
* geodesics,
* and some theorems from global differential geometry.

(19044)

Type

Lecture

Instructor

Prof. Dr. Konrad Polthier, Konstantin Poelke

Language

German

Room

Arnimallee 6

SR 032 (Lecture), SR 009/A6 (Tutorial A), SR 006/T9 (Tutorial B)

Time

* Lecture: Mo + Mi 12 - 14 Uhr

* Tutorials (starting October 15th!):  

* A: Wednesday, 16 - 18h, SR009, A6 (PI Math Building)

* B: Wednesday, 16 - 18h, SR006, T9 (Comp. Science department)

* Exam: Wednesday, 04.02., 12-14h, SR032

* Repeat Exam: Monday, 30.03., 12-14h, SR032

Start

Oct 13, 2014 | 12:00 PM — Feb 11, 2015 | 06:00 PM

Requirements

Analysis I-III,

Linear Algebra I & II

Literature

  • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
  • M. P. doCarmo, 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