English

Finsler geodesics, periodic Reeb orbits, and open books

Dynamical Systems 2019-03-12 v2 Differential Geometry Symplectic Geometry

Abstract

We survey some results on the existence (and non-existence) of periodic Reeb orbits on contact manifolds, both in the open and closed case. We place these statements in the context of Finsler geometry by including a proof of the folklore theorem that the Finsler geodesic flow can be interpreted as a Reeb flow. As a mild extension of previous results we present existence statements on periodic Reeb orbits on contact manifolds with suitable supporting open books.

Keywords

Cite

@article{arxiv.1611.10035,
  title  = {Finsler geodesics, periodic Reeb orbits, and open books},
  author = {Max Dörner and Hansjörg Geiges and Kai Zehmisch},
  journal= {arXiv preprint arXiv:1611.10035},
  year   = {2019}
}

Comments

14 pages; v2: Section 3 added