Conformal vector fields on lcK manifolds

arXiv (Cornell University)（2021）

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Abstract

We show that any conformal vector field on a compact lcK manifold is Killing with respect to the Gauduchon metric. Furthermore, we prove that any conformal vector field on a compact lcK manifold whose K\"ahler cover is neither flat, nor hyperk\"ahler, is holomorphic.

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Key words

conformal vector fields,lck manifolds

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