RECURRENT Z FORMS ON RIEMANNIAN AND KAEHLER MANIFOLDS.

In this paper, we introduce a new kind of Riemannian manifold that generalize the concept of weakly Z-symmetric and pseudo-Z-symmetric manifolds. First a Z form associated to the Z tensor is defined. Then the notion of Z recurrent form is introduced. We take into consideration Riemannian manifolds in which the Z form is recurrent. This kind of manifold is named ()n. The main result of the paper is that the closedness property of the associated covector is achieved also for (Zkl) > 2. Thus the existence of a proper concircular vector in the conformally harmonic case and the form of the Ricci tensor are confirmed for()n manifolds with (Zkl) > 2. This includes and enlarges the corresponding results already proven for pseudo-Z-symmetric ()n and weakly Z-symmetric manifolds ()n in the case of non-singular Z tensor. In the last sections we study special conformally flat ()n and give a brief account of Z recurrent forms on Kaehler manifolds. [ABSTRACT FROM AUTHOR]