Einstein metrics on bundles over hyperKähler manifolds

Abstract

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

30 pages, to appear in Communications in Mathematical Physics

References in corpus (1)

• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries

Cited by in corpus (1)

• Explicit abelian instantons on $S^1$-invariant Kähler Einstein $6$-manifolds