ON CONFORMALLY FLAT LORENTZIAN SPACES SATISFYING A CERTAIN CONDITION ON THE RICCI TENSOR

Abstract

Let M be an n-dimensional complete conformally flat Lorentzian space. If M satisfy the condition R(X, Y)Q = 0, where R is the curvature operator and Q is the Ricci operator of M, respectively, then M is a space of constant curvature, a locally product space of two spaces of constant curvature, or a locally product space of a space of constant curvature and 1-dimensional space.