PT - JOURNAL ARTICLE
AU -
TI - On the global isometric embedding of pseudo-Riemannian manifolds
DP - 1970 Jan 13
TA - Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
PG - 417--428
VI - 314
IP - 1518
4099 - http://rspa.royalsocietypublishing.org/content/314/1518/417.short
4100 - http://rspa.royalsocietypublishing.org/content/314/1518/417.full
SO - Proc R Soc Lond A Math Phys Sci1970 Jan 13; 314
AB - 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.