Strong Kähler with torsion structures from almost contact manifolds

Marisa Fernández, Anna Fino, Luis Ugarte and Raquel Villacampa

Vol. 249 (2011), No. 1, 49–75

DOI: 10.2140/pjm.2011.249.49

Abstract

For an almost contact metric manifold N, we find conditions under which either the total space of an S¹-bundle over N or the Riemannian cone over N admit a strong Kähler with torsion (SKT) structure. In so doing, we construct new 6-dimensional SKT manifolds. Moreover, we study the geometric structure induced on a hypersurface of an SKT manifold and use it to construct new SKT manifolds via appropriate evolution equations. We also study hyper-Kähler with torsion (HKT) structures on the total space of an S¹-bundle over manifolds with three almost contact structures.

Keywords

Hermitian metric, hypercomplex structure, torsion, almost contact structure, Riemannian cone

Mathematical Subject Classification 2000

Primary: 53C55

Secondary: 53C26, 22E25, 53C15

Milestones

Received: 23 September 2009

Accepted: 30 June 2010

Published: 3 January 2011