A Note on Toric Contact Geometry
Differential Geometry
2009-10-31 v2 Symplectic Geometry
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.
Cite
@article{arxiv.math/9907043,
title = {A Note on Toric Contact Geometry},
author = {Charles P. Boyer and Krzysztof Galicki},
journal= {arXiv preprint arXiv:math/9907043},
year = {2009}
}
Comments
Revised version, 10 pages, references added and incorrect statements were corrected