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arXiv · 0812.3002

Transformations of locally conformally Kähler manifolds

Andrei Moroianu·Liviu Ornea
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Abstract

We consider several transformation groups of a locally conformally Kähler manifold and discuss their inter-relations. Among other results, we prove that all conformal vector fields on a compact Vaisman manifold which is neither locally conformally hyperkähler nor a diagonal Hopf manifold are Killing, holomorphic and that all affine vector fields with respect to the minimal Weyl connection of a locally conformally Kähler manifold which is neither Weyl-reducible nor locally conformally hyperkähler are holomorphic and conformal

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Andrei Moroianu, Liviu Ornea. 2009-09-04. Transformations of locally conformally Kähler manifolds. https://doi.org/10.1007/s00229-009-0278-z

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