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Mathematical Geometry Processing

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  • Sommersemester 2015
  • Differential Geometry II

Differential Geometry II

A selection of the following topics:
● Exponential map and the Hopf-Rinow theorem
● Connection between curvature and topology (e.g. Myer's theorem, Hadamard-Cartan, Klingenberg, rigidity theorems)
● Closed geodesics
● Stokes' theorem and Cohomology
● Spaces of constant curvature, Lie groups, homogeneous spaces
● Conformal geometry, geometric differential equations
● Basic notions from differential topology

(19050)

TypeLecture
InstructorProf. Dr. Konrad Polthier
RoomArnimallee 6
StartApr 13, 2015 | 12:00 PM
Time

* Lecture: Mo + We, 12 - 14 h, SR 025/026/A6

* Tutorial: We, 16 - 18 h, SR 032/A6

* Exam: 08.07.15: Wed, 12-14h, SR 025/026

* Retake Exam: Mon, 14.09., 12-14h, SR 032/A6

* Post-exam review (retake): Fri, 18.09., 10-11h, R. 208/A6

Literature

  • Lee, John M., Introduction to Smooth Manifolds, Springer, 2012
  • Lee, John M., Riemannian Manifolds: An Introduction to Curvature, Springer, 1997
  • Kühnel, Wolfgang, Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
  • O'Neill, Barret: Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983

Further Reading:

  • Minimum number of charts for RP^n: http://link.springer.com/chapter/10.1007%2FBFb0085228
  • C1-embedding of the flat torus in R^3: http://math.univ-lyon1.fr/~borrelli/Hevea/Presse/index-en.html

Downloads

  • Exercise Sheet 1
  • Exercise Sheet 2
  • Exercise Sheet 3
  • Exercise Sheet 4
  • Exercise Sheet 5
  • Exercise Sheet 6
  • Exercise Sheet 7
  • Exercise Sheet 8
  • Exercise Sheet 9
  • Exercise Sheet 10
  • Exam 1 - Results
  • Retake Exam - Results

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