%0 Journal Article
%A
%T On the global isometric embedding of pseudo-Riemannian manifolds
%D 1970
%R 10.1098/rspa.1970.0015
%J Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
%P 417-428
%V 314
%N 1518
%X It is shown that any pseudo-Riemannian manifold has (in Nashâ€™s sense) a proper isometric embedding into a pseudo-Euclidean space, which can be made to be of arbitrarily high differentiability. The application of this to the positive definite case treated by Nash gives a new proof using a Euclidean space of substantially lower dimension. The general result is applied to the space-time of relativity, and the dimensions and signatures of the spaces needed to embed various cases are evaluated.
%U http://rspa.royalsocietypublishing.org/content/royprsa/314/1518/417.full.pdf