Strong Kaehler with torsion structures from almost contact manifolds

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For an almost contact metric manifold N, we find conditions for which either the total space of an S¹-bundle over N or the Riemannian cone over N admits a strong Kähler 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-Kähler with torsion (HKT) structures on the total space of an S¹-bundle over manifolds with three almost contact structures are also studied.