Campbell's theorem states that any n -dimensional Riemannian manifold can be embedded locally in an (n + 1)-manifold with a Ricci curvature of R ' a b = 0. The theorem also states, in similar form, that an n -dimensional pseudo-Riemannian manifold can be both locally and isometrically embedded in an n (n + 1)/2- pseudo-Euclidean space.