A classification of Kaehlerian manifolds satisfying some special conditions
type: Item
instance of: scholarly article
title: A classification of Kaehlerian manifolds satisfying some special conditions
zbMATH Open document ID: 0618.53021
DOI: 10.1007/BF01951349
author: Yanyan Li
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53B35
zbMATH DE Number: 4002963
zbMATH Keywords: recurrence condition
zbMATH Keywords: Kaehlerian manifold
zbMATH Keywords: \(BS_ n\)-manifold
zbMATH Keywords: H- projective curvature tensor
zbMATH Keywords: Ricci tensor
zbMATH Keywords: Codazzi tensor
MaRDI profile type: Publication
cites work: On Ruse's Spaces of Recurrent Curvature
cites work: Q5345507
cites work: Q5643228
cites work: Q5333687
cites work: On complex conformal connections
cites work: Q4765240
cites work: Q4057264
cites work: Q5544015
cites work: Curvature and Betti Numbers. II
cites work: Q5532204
cites work: A further method in global differential geometry
description: scientific article; zbMATH DE number 4002963