# Nash Embedding Theorems for Pseudo-Riemannian Manifolds?

Are there analogs of the Nash Embedding Theorems for Pseudo-Riemannian Manifolds?

-
Yes, and the proof much easier, one can explicitly can write a formula for the embedding into $\mathbb{R}^{N,N}$ –  Anton Petrunin Apr 17 at 0:12

See here:

MR0262980 Reviewed Greene, Robert E. Isometric embeddings of Riemannian and pseudo-Riemannian manifolds. Memoirs of the American Mathematical Society, No. 97 American Mathematical Society, Providence, R.I. 1970 iii+63 pp. (Reviewer: W. F. Pohl)

-
Abstract. We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that any $n$-dimensional Riemannian manifold can be locally embedded in an $(n+1)$-dimensional Ricci-flat Riemannian manifold. [...]