Hyperkähler manifolds with torsion obtained from hyperholomorphic bundles

We construct examples of compact hyperkähler manifolds with torsion (HKT manifolds) which are not homogeneous and not locally conformal hyperkähler. Consider a total space T of a tangent bundle over a hyperkähler manifold M . The manifold T is hypercomplex, but it is never hyperkähler, unless M is flat. We show that T admits an HKT-structure. We also prove that a quotient of T by a Z-action v −→ qnv is HKT, for any real number q ∈ R, q > 1. This quotient is compact, if M is compact. A more general version of this construction holds for all hyperholomorphic bundles with holonomy in Sp(n).