Einstein metrics on bundles over hyperKähler manifolds
arXiv:2105.04254 · doi:10.1007/s00220-023-04809-3
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.
arXiv comment30 pages, to appear in Communications in Mathematical Physics
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