It is well known that there are fourteen independent algebraic invariants of the four‐dimensional Riemann tensor. Several authors have written down a set of fourteen independent invariants, but it is still not known how other invariants can be expressed in terms of these sets. This paper investigates this problem by looking for relationships between invariants of the Riemann tensor. Essentially the problem turns out to be analogous to finding relationships between the invariants of two 3×3 matrices, one of which is symmetric and trace‐free and the other Hermitian. A number of identities between the invariants can be obtained simply by using a generalization of the Cayley–Hamilton theorem but others, which depend on the symmetry of the matrices, are considerably more complex.
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February 1996
Research Article|
February 01 1996
The identities of the algebraic invariants of the four‐dimensional Riemann tensor
G. E. Sneddon
G. E. Sneddon
Department of Mathematics and Statistics, James Cook University of North Queensland, Townsville 4811, Australia
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J. Math. Phys. 37, 1059–1075 (1996)
Article history
Received:
July 07 1995
Accepted:
November 09 1995
Citation
G. E. Sneddon; The identities of the algebraic invariants of the four‐dimensional Riemann tensor. J. Math. Phys. 1 February 1996; 37 (2): 1059–1075. https://doi.org/10.1063/1.531425
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