Topics:
We will discuss how one can show the existence of closed resp. periodic geodesics on compact Riemannian anifolds using Morse theory on the free loop space.
In case of positive curvature one can estimate the length of a shortest closed geodesic.
References:
- W.Klingenberg: Riemannian Geometry, 2nd rev. edition, de Gruyter Berlin New York 1995 Springer Link
- A. Oancea: Morse theory, closed geodesics, and the homology of the free loop space, arXiv:1406.3107
(chapter of the book: Free loop spaces in geometry and topology, Editors: Janko Latschev, Alexandru Oancea,
IRMA Lectures in Mathematics and Theoretical Physics 24, European Math. Soc. 2015)
- Trainer/in: Judith Brinkschulte
- Trainer/in: Hans-Bert Rademacher
Semester: WiSe 2023/24