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arXiv · 1803.01363

A characterization of compact locally conformally hyperk\"ahler manifolds

Liviu Ornea·Alexandra Otiman
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Abstract

We give an equivalent definition of compact locally conformally hyperk\"ahler 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 K\"ahler manifold admitting a holomorphic symplectic form is hyperk\"ahler.

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Liviu Ornea, Alexandra Otiman. 2018-03-04. A characterization of compact locally conformally hyperk\"ahler manifolds. https://arxiv.org/abs/1803.01363

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