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Calabi-Yau cones from contact reduction. (English) Zbl 1214.53038

The paper offers a very well structured study of generalized Einstein-Sasaki manifolds. The authors characterize them in terms of both spinors and differential forms, which in the real analytic case correspond to contact manifolds with Calabi-Yau symmetric cone. New seven-dimensional examples of contact \(SU(3)\)-structures associated with a generalized Killing spinor are found. Circle actions that preserve the structure are taken to determine conditions for the contact reduction to carry an induced structure of the same type. By using this method the authors construct more examples and provide an interesting application of their theorem by an original example of a hypo-contact structure on \(S^2\times T^3\).

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D20 Momentum maps; symplectic reduction
53C30 Differential geometry of homogeneous manifolds

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References:

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