On pseudo symmetric spaces
type: Item
instance of: scholarly article
title: On pseudo symmetric spaces
zbMATH Open document ID: 0691.53011
DOI: 10.1007/BF01952047
author: Uday Chand De
author: M. C. Chaki
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: A non-flat Riemannian space whose curvature tensor \(R_{hijk}\) satisfies the condition \[ R_{hijk,\ell}=2\lambda_{\ell}R_{hijk}+\lambda_ hR_{\ell ijk}+\lambda_ iR_{h\ell jk}+\lambda_ jR_{hi\ell k}+\lambda_ kR_{hij\ell}, \] where \(\lambda_ i\) is a non-zero vector and comma denotes covariant differentiation with respect to the metric tensor of the space, is called a pseudo symmetric space, denoted by \((PS)_ n\) and \(\lambda_ i\) is called its associated vector field [the first author, An. Stiint. Univ. Al I. Cuza Iasi, N. Ser., Sect. Ia 33, No.1, 53-58 (1987; Zbl 0626.53037)]. In this paper, the authors study various characterizations of such a pseudo symmetric Riemannian space and discuss the properties of this space and of several vector fields, e.g. the Ricci associate of \(\lambda_ i\), concurrent and recurrent vector fields admitted by \((PS)_ n\), etc.
Mathematics Subject Classification ID: 53B20
zbMATH DE Number: 4131181
zbMATH Keywords: pseudo symmetric space
zbMATH Keywords: associated vector field
zbMATH Keywords: recurrent vector fields
reviewed by: Om Prakash Singh
MaRDI profile type: Publication
cites work: The Riemannian and affine differential geometry of product-spaces
cites work: Q5731354
description: scientific article; zbMATH DE number 4131181