Transformations of locally conformally Kähler manifolds

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

8 pages

References in corpus (1)

• Twistor Forms on Riemannian Products

Cited by in corpus (2)

• Lattices in almost abelian Lie groups with locally conformal Kähler or symplectic structures
• Toric Vaisman Manifolds