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arXiv · 1712.05821

Locally conformally Kähler manifolds with holomorphic Lee field

Andrei Moroianu·Sergiu Moroianu·Liviu Ornea
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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.

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Andrei Moroianu, Sergiu Moroianu, Liviu Ornea. 2017-12-15. Locally conformally Kähler manifolds with holomorphic Lee field. https://doi.org/10.1016/j.difgeo.2018.05.004

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