manuscripta mathematica

, Volume 130, Issue 1, pp 93–100

Transformations of locally conformally Kähler manifolds

Article

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.

Mathematics Subject Classification (2000)

Primary 53C15 53C25 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Centre de MathémathiquesEcole PolytechniquePalaiseau CedexFrance
  2. 2.Faculty of MathematicsUniversity of BucharestBucharestRomania
  3. 3.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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