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 Web Resource. https://mathworld.wolfram.com/CampbellsTheorem.html