Are there analogs of the Nash Embedding Theorems for PseudoRiemannian Manifolds?

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


Not clear where you are headed with your concise question, but if you have any interest in Lorenzian manifolds as instances of pseudoRiemannian manifolds, then this might be of interest, especially for the theorem of Campbell: "The embedding of General Relativity in five dimensions." Carlos Romero, Reza Tavakol, Roustam Zalaletdinov. General Relativity and Gravitation. March 1996, Volume 28, Issue 3, pp 365376. (Springer link.)
And there are many papers in some sense following, e.g.: "The embedding of space–times in five dimensions with nondegenerate Ricci tensor," F. Dahia and C. Romero, J. Math. Phys. 43, 3097 (2002). (AIP link.) 

