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Dimensionally dependent identities

Published online by Cambridge University Press:  24 October 2008

David Lovelock
David Lovelock
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
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Abstract

In the general theory of relativity a number of apparently unrelated identities peculiar to a 4-dimensional space are frequently used. However, the proofs usually presented appear to have no common ideas and, furthermore, it is not clear at what stage the dimensionality restriction plays a significant role. In this note a technique is presented which explicitly exhibits the dimensionality dependence and thereby enables the above identities to be generalized for n-dimensional spaces. It is also shown that the above identities are all special cases of a more general identity valid for n = 4.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 345 - 350
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

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