Campbell's theorem states that 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.
Campbell's Theorem
See also
Embedding, Pseudo-Euclidean Space, Pseudo-Riemannian Manifold, Ricci Curvature Tensor, Riemannian ManifoldExplore with Wolfram|Alpha
References
Eisenhart, L. P. Riemannian Geometry. Princeton, NJ: Princeton University Press, 1964.Referenced on Wolfram|Alpha
Campbell's TheoremCite this as:
Weisstein, Eric W. "Campbell's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CampbellsTheorem.html