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Einstein Metrics on Bundles over Hyperkähler Manifolds

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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.

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Acknowledgements

The author would like to thank Simon Salamon for introducing to him the beautiful geometry of quaternion-Kähler manifolds and also for many useful comments that helped shape this article. We would also like to thank Vicente Cortés for interesting remarks that led to the results in Sect. 6. This work was partly supported by the São Paulo Research Foundation (FAPESP) [2021/07249-0].

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  1. IMECC - Unicamp, Rua Sérgio Buarque de Holanda, 651, Campinas, SP, 13083-859, Brazil

    Udhav Fowdar

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Fowdar, U. Einstein Metrics on Bundles over Hyperkähler Manifolds. Commun. Math. Phys. 403, 1–35 (2023). https://doi.org/10.1007/s00220-023-04809-3

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