Strong Kaehler with torsion structures from almost contact manifolds

TL;DR

This paper explores conditions under which certain geometric constructions over almost contact manifolds yield strong Kähler with torsion (SKT) structures, leading to new 6-dimensional SKT manifolds and insights into related HKT structures.

Contribution

It introduces new methods to construct SKT and HKT manifolds from almost contact and contact structures, expanding the class of known SKT manifolds.

Findings

Conditions for SKT structures on $S^1$-bundles and cones over almost contact manifolds

Construction of new 6-dimensional SKT manifolds

Analysis of induced structures on hypersurfaces of SKT manifolds

Abstract

For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new 6-dimensional SKT manifolds. Moreover, we study the geometric structure induced on a hypersurface of an SKT manifold, and use such structures to construct new SKT manifolds via appropriate evolution equations. Hyper-K\"ahler with torsion (HKT) structures on the total space of an $S^1$-bundle over manifolds with three almost contact structures are also studied.