Transformations of locally conformally Kähler manifolds

Andrei Moroianu (1) , Liviu Ornea (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 UNIBUC - Université de Bucarest

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

Mots clés: Killing vector field; conformal vector field; affine transformation; locally conformally Kähler manifold; Gauduchon metric

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu, Liviu Ornea. Transformations of locally conformally Kähler manifolds. Manuscripta mathematica, 2009, 130 (1), pp.93-100. ⟨10.1007/s00229-009-0278-z⟩. ⟨hal-00347485v2⟩