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On the classification of isotropic tensors

Published online by Cambridge University Press:  18 May 2009

P. G. Appleby ,
B. R. Duffy  and
R. W. Ogden
P. G. Appleby
Affiliation:
University of Liverpool, Department Of Applied Mathematics and Theoretical Physics, P.O. Box 147, Liverpool L69 3BX
B. R. Duffy
Affiliation:
University of Strathclyde, Department of Mathematics, Livingstone Tower, 26 Richmond Street, Glasgow Gl 1XH
R. W. Ogden
Affiliation:
University of Glasgow, Department of Mathematics, Glasgow G12 8QW
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A tensor is said to be isotropic relative to a group of transformations if its components are invariant under the associated group of coordinate transformations. In this paper we review the classification of tensors which are isotropic under the general linear group, the special linear (unimodular) group and the rotational group. These correspond respectively to isotropic absolute tensors [4, 8] isotropic relative tensors [4] and isotropic Cartesian tensors [3]. New proofs are given for the representation of isotropic tensors in terms of Kronecker deltas and alternating tensors. And, for isotropic Cartesian tensors, we provide a complete classification, clarifying results described in [3].

In the final section of the paper certain derivatives of isotropic tensor fields are examined.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 2 , July 1987 , pp. 185 - 196
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

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