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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


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 assignements are needed.
InstructorProf. Dr. Konrad Polthier, Henriette Lipschütz
Credit Points10
RoomArnimallee 6
StartApr 16, 2018

*Lecture: Monday, 12-14, 007/008/A6, Wednesday, 12-14, 007/008/A6

*Tutorials: Friday, 10-12, 032/A6

*Exams: first July, 20th, 2018. Dates will be given on request.

              second: tba


The lectures and the tutorials will be held in English on request.


  • 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
  • Guillemin, Victor and Pollack, Alan: Differential Topology, AMS Chelsea Publishing, 2010
  • Hirsch, Morris: Differential Topology, Graduate Texts in Mathematics, Springer, 1997
  • Kreck, Matthias: Differential Algebraic Topology, Graduate Studies in Mathematics, Band 110, AMS, 2010
  • Munkres, James: Topology, Pearson New International Edition, 2013

Further Reading: