Toric Surfaces and Sasakian-Einstein 5-manifolds

Details Toric Surfaces and Sasakian-Einstein 5-manifolds Toric Surfaces and Sasakian-Einstein 5-manifolds

2006-07-27

arxiv.org/abs/math/0607721v1

Mathematics

Differential Geometry

71 pages

Scientific paper

This article gives a construction of toric Sasakian-Einstein structures on k#(S^2 xS^3) for odd k. For each odd k>1 this method constructs countably infinitely many toric Sasakian-Einstein structures on k#(S^2 xS^3). These are submanifolds of the toric 3-Sasakian 7-manifolds produced by 3-Sasakian reduction by K. Galicki, C. Boyer and others, and this is one ingredient in the construction. This article includes much of the toric geometry and 3-Sasakian geometry that is used in the proof. It is essentially the authors Ph.D. dissertation.

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