Campbell's Theorem

Any n-dimensional Riemannian manifold can be locally embedded into an (n+1)-dimensional manifold with Ricci curvature Tensor R_(ab)=0. A similar version of the theorem for a pseudo-Riemannian manifold states that any n-dimensional pseudo-Riemannian manifold can be locally and isometrically embedded in an n(n+1)/2-dimensional pseudo-Euclidean space.

See also

Embedding, Pseudo-Euclidean Space, Pseudo-Riemannian Manifold, Ricci Curvature Tensor, Riemannian Manifold

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

Referenced on Wolfram|Alpha

Campbell's Theorem

Cite this as:

Weisstein, Eric W. "Campbell's Theorem." From MathWorld--A Wolfram Web Resource.

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