On semisymmetric para-Kähler manifolds
type: Item
instance of: scholarly article
title: On semisymmetric para-Kähler manifolds
zbMATH Open document ID: 0922.53009
DOI: 10.1007/BF02697871
published in: Acta Mathematica Hungarica
publication date: 1999-09-14T00:00:00Z
review text: The main results in the paper are: Theorem 3.3. Every Ricci-generalized pseudosymmetric para-Kähler manifold \((M,g,I)\), \(\dim M\geq 4\), is Ricci-semisymmetric. Theorem 4.1. Every para-Kähler hypersurface of a semi-Euclidean space \(E^{2m+1}_u\), \(m\geq 2\), of index \(u\), is semisymmetric.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 1336322
zbMATH Keywords: para-Kähler manifold
zbMATH Keywords: semisymmetric connection
zbMATH Keywords: pseudosymmetric manifold
author: Filip Defever
author: Ryszard Deszcz
author: Leopold Verstraelen
reviewed by: Grozio Stanilov
MaRDI profile type: Publication
cites work: Q3357023
cites work: Pseudosymmetry curvature conditions imposed on the shape operators of hypersurfaces in the affine space
cites work: Q4299172
cites work: Lorentzian isoparametric hypersurfaces
cites work: Complete Hypersurfaces with RS = 0 In E n+1
cites work: On generalized curvature tensors on some Riemannian manifolds
cites work: Hypersurfaces with parallel Ricci tensor
cites work: A class of complex hypersurfaces
cites work: Almost Hermitian manifolds with constant holomorphic sectional curvature
cites work: Structure theorems on Riemannian spaces satisfying \(R(X,Y)\cdot R=0\). I: The local version
cites work: Hypersurfaces satisfying a certain condition on the Ricci tensor
cites work: Q4867785
description: scientific article; zbMATH DE number 1336322