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A Note on Toric Contact Geometry

Charles P. Boyer·Krzysztof Galicki
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Abstract

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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Charles P. Boyer, Krzysztof Galicki. 1999-09-29. A Note on Toric Contact Geometry. https://doi.org/10.1016/s0393-0440(99)00078-9

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