Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators
Conformally Flat Semi-Riemannian Manifolds with Commuting Curvature and Ricci Operators
We classify the conformally flat, semi-Riemannian manifolds satisfying R(X, Y ) • 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 …