Hyperkaehler manifolds with torsion obtained from hyperholomorphic bundles

We construct examples of compact hyperkaehler manifolds with torsion (HKT manifolds) which are not homogeneous and not locally conformal hyperkaehler. Consider a total space T of a tangent bundle over a hyperkaehler manifold M. The manifold T is hypercomplex, but it is never hyperkaehler, unless M is flat. We show that T admits an HKT-structure. We also prove that a quotient of T by a $\mathbb{Z}$-action $v\text{arrow}{q}^{n}v$ is HKT, for any real number $q\in \mathbb{R}$, $q>1$. 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).