Perfect Reeb Flows And Action–Index Relations

Keywords

Contact forms; Contact homology; Periodic orbits; Reeb flows

Abstract

We study non-degenerate Reeb flows arising from perfect contact forms, i.e., the forms with vanishing contact homology differential. In particular, we obtain upper bounds on the number of simple closed Reeb orbits for such forms on a variety of contact manifolds and certain action–index resonance relations for the standard contact sphere. Using these results, we reprove a theorem due to Bourgeois, Cieliebak and Ekholm characterizing perfect Reeb flows on the standard contact three-sphere as non-degenerate Reeb flows with exactly two simple closed orbits.

Publication Date

2-1-2015

Publication Title

Geometriae Dedicata

Volume

174

Issue

1

Number of Pages

105-120

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10711-014-0006-z

Socpus ID

84921888903 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84921888903

This document is currently not available here.

Share

COinS