An Example of a Concircular Vector Field on a Locally Conformally Kähler Manifold

An example of a concircular vector field on a locally conformally Kähler manifold is constructed and the geometric meaning of its characteristic form is studied. It is proved that the Lie vector of a locally conformally Kähler manifold of constant curvature is a concircular vector field. It is also shown that the class of locally conformally Kähler manifolds of constant curvature is a subclass of the class of locally concircularly nearly Kähler manifolds. Conditions under which a locally conformally Kähler manifold of constant curvature is recurrent are obtained.