Hyperkaehler manifolds with torsion obtained from hyperholomorphic bundles

الأصل · EN

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 -action v qⁿ v is HKT, for any real number q∈, 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).