Open problems and questions about geodesics

Keith Burns, Vladimir S. Matveev

Research output: Contribution to journalReview articlepeer-review

17 Scopus citations

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 languageEnglish (US)
Pages (from-to)641-684
Number of pages44
JournalErgodic Theory and Dynamical Systems
Volume41
Issue number3
DOIs
StatePublished - 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

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