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)

Type

Lecture

Instructor

Prof. Dr. Konrad Polthier, Konstantin Poelke

Room

Arnimallee 6

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

Start

Apr 13, 2015 | 12:00 PM

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: