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arXiv · 2105.04254

Einstein metrics on bundles over hyperK\"ahler manifolds

Udhav Fowdar
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Abstract

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

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Udhav Fowdar. 2021-05-10. Einstein metrics on bundles over hyperK\"ahler manifolds. https://doi.org/10.1007/s00220-023-04809-3

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