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The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed

Abstract : A classical theorem due to Wadsley implies that, on a contact manifold all of whose Reeb orbits are closed, there is a common period for the Reeb orbits. In this paper we show that, for any Reeb flow on a closed 3-manifold, the following conditions are actually equivalent: (1) every Reeb orbit is closed; (2) all closed Reeb orbits have a common period; (3) the action spectrum has rank 1. We also show that, on a fixed closed 3-manifold, a contact form with an action spectrum of rank 1 is determined (up to pull-back by diffeomorphisms) by the set of minimal periods of its closed Reeb orbits.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-02352678
Contributor : Marco Mazzucchelli <>
Submitted on : Thursday, November 7, 2019 - 12:56:29 AM
Last modification on : Wednesday, December 2, 2020 - 12:19:54 AM

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Daniel Cristofaro-Gardiner, Marco Mazzucchelli. The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed. Commentarii Mathematici Helvetici, European Mathematical Society, 2020, 95 (3), pp.461-481. ⟨10.4171/CMH/493⟩. ⟨ensl-02352678⟩

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