Locally conformally Kähler manifolds with holomorphic Lee field

Abstract

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free). We also give examples of compact lcK manifolds with holomorphic Lee vector field which are not Vaisman.

6 pages

References in corpus (1)

• On toric locally conformally Kähler manifolds

Cited by in corpus (1)

• LcK structures with holomorphic Lee vector field on Vaisman-type manifolds