Einstein Metrics on Bundles over Hyperkähler Manifolds

We construct explicit examples of quaternion-Kahler and hypercomplex structures on bundles over hyperKahler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki-Lawson quaternion-Kahler moment map. By performing the QK reduction we produce several explicit QK metrics. Moreover we are led to a new proof of a hyperKahler/quaternion-Kahler type correspondence. We also give examples of other Einstein metrics and balanced Hermitian structures on these bundles.