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On isotropic tensors

Published online by Cambridge University Press:  24 October 2008

Harold Jeffreys
Harold Jeffreys
Affiliation:
St John's College, Cambridge
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Extract

1. An isotropic tensor is one the values of whose components are unaltered by any rotation of rectangular axes (with metric σi(dxi)2). Those up to order 4 in 2 and 3 dimensions have many applications. The results suggest a general theorem for tensors of order m in n dimensions, that any isotropic tensor can be expressed as a linear combination of products of δ and є tensors, where δij = 1 if i = j and 0 otherwise, and is 0 if any two of the i1 to in are equal, 1 if i1…in is an even permutation of 1, 2, 3, …,n, and – 1 if it is an odd permutation.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 173 - 176
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

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