A characterization of compact locally conformally hyperk\"ahler manifolds

19 Jun 2018 · Ornea Liviu, Otiman Alexandra ·

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.