Campbell's Theorem

Any -dimensional Riemannian manifold can be locally embedded into an -dimensional manifold with Ricci curvature Tensor . A similar version of the theorem for a pseudo-Riemannian manifold states that any -dimensional pseudo-Riemannian manifold can be locally and isometrically embedded in an -dimensional pseudo-Euclidean space.

REFERENCES:

Eisenhart, L. P. Riemannian Geometry. Princeton, NJ: Princeton University Press, 1964.