Proper curvature collineations in Bianchi type I space-times
type: Item
instance of: scholarly article
title: Proper curvature collineations in Bianchi type I space-times
zbMATH Open document ID: 1058.83025
author: Ghulam Shabbir
published in: Gravitation \& Cosmology
publication date: 2004-11-16T00:00:00Z
review text: The author studies Bianchi type I space-times according to their proper curvature collineations (CCs). These curvature collineations are vector fields along which the Lie derivative of the Riemann tensor is zero. An approach is adopted connected with using the rank of the \(6\times6\) Riemann matrix, direct integration techniques, and also the theorem given in \textit{G.~S.~Hall} and \textit{J.~ da Costa} [J. Math. Phys. 32, 2848--2853 (1991; Zbl 0745.53019) and 32, 2854 (1991; Zbl 0745.53020)], which described where proper CCs exist. The classification of the Riemann tensor in terms of its rank and bivector decomposition, and classification of space-times in terms of curvature collineations are given. It is shown that when the above space-times admit proper curvature collineations, they form an infinite-dimensional vector space.
Mathematics Subject Classification ID: 83F05
Mathematics Subject Classification ID: 53B30
zbMATH DE Number: 2115960
zbMATH Keywords: proper curvature collineations
zbMATH Keywords: Bianchi type I space-times
zbMATH Keywords: two-dimensional submanifolds
zbMATH Keywords: positive definite metric
zbMATH Keywords: Lorentzian metric
zbMATH Keywords: Killing vector fields
zbMATH Keywords: Lie derivative
zbMATH Keywords: rank of Riemann tensor
zbMATH Keywords: bivector decomposition
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2115960