A note on proper curvature symmetry in general cylindrically symmetric four-dimensional Lorentzian manifolds

Abstract

We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the [Formula: see text] Riemann matrix and direct integration techniques. Studying proper curvature symmetry in each case of the above space-times, we show that when the above space-times admit proper curvature symmetry, they form an infinite dimensional vector space. It is important to note that here we also find the case when the rank of the [Formula: see text] Riemann matrix is one and no covariantly constant vector fields exist.