A Note on Toric Contact Geometry

Details A Note on Toric Contact Geometry A Note on Toric Contact Geometry

1999-07-07

arxiv.org/abs/math/9907043v2

Jour. Geom. and Phys. 35 (2000), 288-298

Mathematics

Differential Geometry

Revised version, 10 pages, references added and incorrect statements were corrected

Scientific paper

10.1016/S0393-0440(99)00078-9

After observing that the well-known convexity theorems of symplectic geometry also hold for compact contact manifolds with an effective action of a torus whose Reeb vector field corresponds to an element of the Lie algebra of the torus, we use this fact together with a recent symplectic orbifold version of Delzant's theorem due to Lerman and Tolman [LT] to show that every such compact toric contact manifold can be obtained by a contact reduction from an odd dimensional sphere.

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