Proper curvature collineations in Bianchi type I space-times
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.
scientific article; zbMATH DE number 2115960