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Transformations of locally conformally Kähler manifolds

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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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Authors and Affiliations

  1. Centre de Mathémathiques, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Andrei Moroianu

  2. Faculty of Mathematics, University of Bucharest, 14 Academiei str., 70109, Bucharest, Romania

    Liviu Ornea

  3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21, Calea Grivitei str., 010702, Bucharest, Romania

    Liviu Ornea

Authors
  1. Andrei Moroianu
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  2. Liviu Ornea
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Corresponding author

Correspondence to Andrei Moroianu.

Additional information

This work was accomplished in the framework of the Associated European Laboratory “MathMode”. L. Ornea is partially supported by CNCSIS PNII grant code 8.

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Moroianu, A., Ornea, L. Transformations of locally conformally Kähler manifolds. manuscripta math. 130, 93–100 (2009). https://doi.org/10.1007/s00229-009-0278-z

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  • DOI: https://doi.org/10.1007/s00229-009-0278-z

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