We classify the conformally flat, semi-Riemannian manifolds satisfying $R(X,Y) \cdot Q = 0$, where $R$ and $Q$ are the curvature tensor and the Ricci operator, respectively. As the cases which do not occur in the Riemannian manifolds, the Ricci operator $Q$ has pure imaginary eigenvalues or it satisfies $Q^2 = 0$.
"Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators." Tokyo J. Math. 26 (1) 241 - 260, June 2003. https://doi.org/10.3836/tjm/1244208691