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 language||English (US)|
|Number of pages||11|
|Journal||Mathematical Research Letters|
|State||Published - 2002|
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