Abstract
It is shown that any pseudo-Riemannian manifold has (in Nash’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.
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Schedule a callMore From: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
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