A characterization of compact locally conformally hyperkähler manifolds

Ornea, Liviu; Otiman, Alexandra

doi:10.1007/s10231-019-00829-w

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A characterization of compact locally conformally hyperkähler manifolds

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Otiman, Alexandra
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s10231-019-00829-w
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arXiv:1803.01363.pdf
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Ornea, L., & Otiman, A. (2019). A characterization of compact locally conformally hyperkähler manifolds. Annali di Matematica Pura ed Applicata, 198(5), 1541-1549. doi:10.1007/s10231-019-00829-w.

Cite as: https://hdl.handle.net/21.11116/0000-0005-0BE4-E

Abstract

We give an equivalent definition of compact locally conformally hyperkähler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that a compact Kähler manifold admitting a holomorphic symplectic form is
hyperkähler.