Calabi-Yau cones from contact reduction

Details Calabi-Yau cones from contact reduction Calabi-Yau cones from contact reduction

2007-10-24

arxiv.org/abs/0710.4441v2

Annals of Global Analysis and Geometry, 2010, Volume 38, Number 1, Pages 93-118

Mathematics

Differential Geometry

30 pages; v2: typos corrected, presentation improved, one reference added. To appear in Ann. Glob. Analysis and Geometry

Scientific paper

10.1007/s10455-010-9202-8

We consider a generalization of Einstein-Sasaki manifolds, which we characterize in terms both of spinors and differential forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We construct solvable examples in seven dimensions. Then, we consider circle actions that preserve the structure, and determine conditions for the contact reduction to carry an induced structure of the same type. We apply this construction to obtain a new hypo-contact structure on S^2\times T^3.

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