2003/03/11 by Misha Verbitsky
Mathematics · #math.DG #math.AG
published as Math. Res. Lett. 10 (2003), no. 4, 501--513. · 17 pages, LaTeX
arxiv created 2003/03/11 · arxiv updated 2009/11/30
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 \Z-action v \arrow qn v 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).