Calabi-Yau cones from contact reduction

TL;DR

This paper generalizes Einstein-Sasaki manifolds using contact reduction, constructs examples in seven dimensions, and introduces new structures on S^2×T^3 through symmetry-preserving reductions.

Contribution

It characterizes a broader class of contact manifolds with Calabi-Yau cones and provides explicit constructions and reductions leading to new geometric structures.

Findings

Constructed solvable 7D examples of generalized Einstein-Sasaki manifolds.

Derived conditions for contact reduction to preserve geometric structures.

Obtained a new hypo-contact structure on S^2×T^3.

Abstract

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.