Finsler geodesics, periodic Reeb orbits, and open books

2016/11/30 by Max Dörner, Hansjörg Geiges, Kai Zehmisch · 2 citations
Mathematics · #math.DS #math.DG #math.SG #msc:37J45 #msc:37C27 #msc:53B40 #msc:53D25 #msc:53D35

paper · pdf · doi:10.1007/s40879-017-0158-0

published as Eur. J. Math. 3 (2017), 1058-1075 · 14 pages; v2: Section 3 added

arxiv created 2017/05/08 · arxiv updated 2019/03/12

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.

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