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On the problem of algebraic completeness for the invariants of the Riemann tensor. III.

Carminati, John and Zakhary, Emil 2002, On the problem of algebraic completeness for the invariants of the Riemann tensor. III., Journal of mathematical physics, vol. 43, no. 8, pp. 4020-4034.

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Title On the problem of algebraic completeness for the invariants of the Riemann tensor. III.
Author(s) Carminati, John
Zakhary, Emil
Journal name Journal of mathematical physics
Volume number 43
Issue number 8
Start page 4020
End page 4034
Publisher American Institute of Physics
Place of publication New York, N.Y.
Publication date 2002-08
ISSN 0022-2488
1089-7658
Summary We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.
Language eng
Field of Research 010102 Algebraic and Differential Geometry
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2002, American Institute of Physics
Persistent URL http://hdl.handle.net/10536/DRO/DU:30001458

Document type: Journal Article
Collection: School of Information Technology
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