Periodic Reeb orbits on prequantization bundles

Peter Albers; Jean Gutt; Doris Hein

doi:10.3934/jmd.2018005

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2018, Volume 12: 123-150. Doi: 10.3934/jmd.2018005

This volume Previous Article The mapping class group of a shift of finite type Next Article Distortion and the automorphism group of a shift

Periodic Reeb orbits on prequantization bundles

1.
Mathematisches Institut, Universität Heidelberg, Mathematikon, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
2.
Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany
3.
Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Ernst-Zermelo-Straße 1, D-79104 Freiburg, Germany

Received: January 16, 2017

Revised: January 15, 2018

Published: April 2018

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Abstract

In this paper, we prove that every graphical hypersurface in a prequantization bundle over a symplectic manifold $M$, pinched between two circle bundles whose ratio of radii is less than $\sqrt{2}$ carries either one short simple periodic orbit or carries at least cuplength $(M)+1$ simple periodic Reeb orbits.

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Mathematics Subject Classification: Primary: 53D10; Secondary: 37J45.

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Figure 1. The function $h$. The numbers at the graph indicate the slope at this point/section

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Figure 2. The moduli space at $\rho = 0$

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Figure 3. The moduli space at $\rho>0$

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