Locally conformally K\"ahler manifolds with holomorphic Lee field
Differential Geometry
2019-01-08 v1
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.
Keywords
Cite
@article{arxiv.1712.05821,
title = {Locally conformally K\"ahler manifolds with holomorphic Lee field},
author = {Andrei Moroianu and Sergiu Moroianu and Liviu Ornea},
journal= {arXiv preprint arXiv:1712.05821},
year = {2019}
}
Comments
6 pages