Abstract
The paper surveys open problems and questions related to geodesics defined by Riemannian, Finsler, semi-Riemannian and magnetic structures on manifolds. It is an extended report on problem sessions held during the International Workshop on Geodesics in August 2010 at the Chern Institute of Mathematics in Tianjin.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 641-684 |
| Number of pages | 44 |
| Journal | Ergodic Theory and Dynamical Systems |
| Volume | 41 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 2021 |
Funding
Acknowledgements. This paper is an extended report on problem sessions held during the International Workshop on Geodesics in August 2010 at the Chern Institute of Mathematics in Tianjin. The focus of the conference was on geodesics in smooth manifolds. It was organized by Victor Bangert and Yiming Long and supported by AIM, CIM, and NSF. We thank all the participants, especially Victor Bangert, Charles Boubel, Nancy Hingston, Gerhard Knieper, Yiming Long, Gabriel Paternain, Mark Pollicott, Regina Rotman, Stéphane Sabourau and Benjamin Schmidt, for active participation in the problem sessions. We also thank non-participants who have helped: Alberto Abbondandolo, Juan-Carlos Alvarez Paiva, Ivan Babenko, Florent Balacheff, Helga Baum, Michael Bialy, Dima Burago, Maciej Dunajski, Misha Gromov, Larry Guth, Sergei Ivanov, Bruce Kleiner, Alan Reid and Stefan Suhr. Most of the writing of the paper was done during four visits by KB to the Friedrich-Schiller-Universität Jena, supported by DFG (SPP 1154 and GK 1523).
Keywords
- closed geodesic
- entropy
- geodesics
- integrable geodesic flows
- projectively equivalent metrics
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics