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