Completely integrable torus actions on symplectic cones

Eugene Lerman, Nadya Shirokova

Research output: Contribution to journalArticlepeer-review

Abstract

We study completely integrable torus actions on symplectic cones (equivalently, completely integrable torus actions on contact manifolds). We show that if the cone in question is the punctured cotangent bundle of a torus then the action has to be free. From this it follows easily, using hard results of Marie and of Burago and Ivanov, that a metric on a torus whose geodesic flow admits global action-angle coordinates is necessarily flat thereby proving a conjecture of Toth and Zelditch.

Original languageEnglish (US)
Pages (from-to)105-115
Number of pages11
JournalMathematical Research Letters
Volume9
Issue number1
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)

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