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Differential Geometry II

In the lecture, basic topics in Riemannian Geometry are treated from a theoretical point of view and illustrated with several examples.

Content: A digest of the following topics will be presented:

  • Exponential map and Hopf-Rinow theorem
  • Connections between curvature und topology (e.g. Myers theorem, Hadamard-Cartan theorem, Klingenberg theorem, rigidity theorems)
  • Closed geodesics
  • Stokes theorem, cohomology
  • Spaces of constant curvature, Lie groups, symmetric and homogeneous spaces
  • Conformal geometry, geometric evolution equations and differential equations from geometric analysis
  • Basic concepts from differential topology

(19214301)

To achieve regular and active participation it is necessary to visit at least 75% of the offered tutorials and to earn at least 60% of the possible points on the exercise sheets.
TypeLecture with exercise session
InstructorProf. Dr. Konrad Polthier, Eric Zimmermann
LanguageEnglish
Credit Points10
StartApr 16, 2022 | 12:00 PM
endJul 18, 2022 | 02:00 PM
Time
  • Lecture: Tuesday and Thursday, both 12:00-14:00 in A6/SR 025/026 (Arnimallee 6); (starting April, 16th, 2024)
  • Exercise Session: Friday, 10:00-12:00; A7/SR 031 (Arnimallee 7); (starting April 26th, 2024)
  • Exam 1: t.b.a.
  • Exam 2: t.b.a.
Note

Precondition: Differential Geometry I

Literature

  • Wolfgang Kühnel - Differentialgeometrie (English version: Differential Geometry)
  • Barrett O'Neill - Semi-Riemannian Geometry
  • Paul Petersen - Riemannian Geometry
  • Georg Glaeser, Konrad Polthier - Bilder der Mathematik

Exercise Sheets

  • tba