On some pseudosymmetry type curvature condition.
type: Item
instance of: scholarly article
title: On some pseudosymmetry type curvature condition.
zbMATH Open document ID: 1047.53040
author: Ryszard Deszcz
author: Marian Hotloś
published in: Tsukuba Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: In several papers the authors and some of their collaborators published already a series of results concerning pseudo-Riemannian manifolds satisfying some ``pseudo-symmetry'' curvature condition. In this paper they continue this research. Let \((M, g)\) be a pseudo-Riemannian manifold, \(R\) its curvature tensor and \(C\) the corresponding Weyl tensor. They study manifolds \((M,g)\) such that \(R\cdot C-C\cdot R\) and the tensor \(Q(g,R)\), which they defined in earlier papers, are linearly dependent at any point of \(M\). Here \(R\) and \(C\) act as derivations. Their main result is that such manifolds must be semi-symmetric, i.e. \(R\cdot R= 0\), a condition which provided the starting point of their research on this type of conditions. Furthermore, they provide some examples of semi-symmetric warped products which satisfy the relation mentioned above and which illustrate their search for a possible inverse of their main result.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 1998401
zbMATH Keywords: curvature tensor
zbMATH Keywords: Weyl tensor
zbMATH Keywords: semi-symmetric
zbMATH Keywords: warped product
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496164557
OpenAlex ID: W1525091207
Wikidata QID: Q124963894
DOI: 10.21099/TKBJM/1496164557
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description: scientific article; zbMATH DE number 1998401