A characterization of compact locally conformally hyperk\"ahler manifolds
Differential Geometry
2020-07-30 v2
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.
Keywords
Cite
@article{arxiv.1803.01363,
title = {A characterization of compact locally conformally hyperk\"ahler manifolds},
author = {Liviu Ornea and Alexandra Otiman},
journal= {arXiv preprint arXiv:1803.01363},
year = {2020}
}
Comments
We simplified the hypothesis and the proof of the main result