Geodesic
Imbedding of pseudo-Riemannian manifolds in a pseudo-euclidean space
Matematičeskie zametki, Tome 9 (1971) no. 2, pp. 193-198.

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It is proved that every pseudo-Riemannian manifold $M^n_{(p,q)}$ with the $C^k$ metric ($3\leqslant k\leqslant\infty$) has an isometric $C^k$ imbedding in the large in $E_{(p',q')}^{n(n+1)(3n+11)/2}$, $p'\geqslant(n+1)^2$, $q'\geqslant(n+1)^2$. 
@article{MZM_1971_9_2_a9,
     author = {D. D. Sokolov},
     title = {Imbedding of {pseudo-Riemannian} manifolds in a pseudo-euclidean space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {193--198},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_2_a9/}
}
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D. D. Sokolov. Imbedding of pseudo-Riemannian manifolds in a pseudo-euclidean space. Matematičeskie zametki, Tome 9 (1971) no. 2, pp. 193-198. http://geodesic.mathdoc.fr/item/MZM_1971_9_2_a9/