A classification of Kaehlerian manifolds satisfying some special conditions
A Kaehlerian manifold, \(K^ m\), is called: BS\({}_ n\)-manifold if the Bochner curvature tensor is parallel \((B^ h_{kji,l}=0)\), symmetric in the sense of Cartan (resp. H-projective symmetric) if the Riemannian curvature tensor (resp. H-projective curvature tensor) is parallel, Ricci-recurrent if the Ricci tensor is non zero and is recurrent (that is, \(R_{ij,l}=A_ lR_{ij}\) for a nonzero vector A). A symmetric tensor T is called a Codazzi tensor if \(T_{ij,k}=T_{ik,j}.\) The main result is: Theorem 4.1. In a \(BS_ n\)-manifold whose Ricci tensor is Codazzi and recurrent the following cases occur: i) the manifold has vanishing Bochner curvature tensor and is recurrent, ii) the manifold is symmetric in the sense of Cartan and \(R_{ij}=0\), iii) the scalar curvature vanishes and the recurrence vector \(A_ 1\) is null.
scientific article; zbMATH DE number 4002963