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Inhalt: Auswahl aus folgenden Themen:

  • Exponentialabbildung und der Satz von Hopf-Rinow
  • Riemann'sche Mannidfaltigkeiten und Metriken, Riemann'scher Krümmungstensor
  • Levi-Civita-Zusammenhang
  • Zusammenhänge zwischen Krümmung und Topologie (z. B. Satz von Myers, Hadamard-Cartan, Klingenberg, Starrheitssätze)
  • geschlossene Geodäten
  • Satz von Stokes, Kohomologie
  • Räume konstanter Krümmung, Lie-Gruppen, symmetrische und homogene Räume
  • Diskretisierung, numerische Anwendungen

Literatur wird in der Vorlesung bekanntgegeben.

Aktuelle Informationen finden sich auf der Kursseite der AG:

http://www.mi.fu-berlin.de/en/math/groups/ag-geom/teaching/18_SoSe/DifferentialGeometryII/index.html

Content: digest of the following topics:

  • exponential map and Hopf-Rinow theorem
  • Riemannian manifolds and metrics, Riemannian curvature tensor
  • Levi-Civita connection
  • connections between curvature und topology (Myers theorem, Hadamard-Cartan theorem, Klingenberg theorem, rigidity theorems)
  • closed geodesics
  • Stokes theorem, cohomology
  • spaces of constant curvature, Lie groups, symmetric and homogeneous spaces
  • discretization, numerical application

Literature: will be announced in the lecture.

Actual infromation can be found on the course webpage of the working group:

http://www.mi.fu-berlin.de/en/math/groups/ag-geom/teaching/18_SoSe/DifferentialGeometryII/index.html

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