1. Transformations of locally conformally Kähler manifolds
- Author
-
Andrei Moroianu and Liviu Ornea
- Subjects
Mathematics - Differential Geometry ,Connection (fibred manifold) ,Quantitative Biology::Biomolecules ,Pure mathematics ,Hopf manifold ,Mathematics::Complex Variables ,General Mathematics ,Holomorphic function ,Conformal map ,Kähler manifold ,Algebraic geometry ,Manifold ,Vector field ,Mathematics::Differential Geometry ,53C15, 53C25 ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
We consider several transformation groups of a locally conformally K\"ahler 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 hyperk\"ahler 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 K\"ahler manifold which is neither Weyl-reducible nor locally conformally hyperk\"ahler are holomorphic and conformal, Comment: 8 pages
- Published
- 2009
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