(Conformally) semisymmetric spaces and special semisymmetric Weyl tensors

Semisymmetric spaces are a natural generalisation of symmetric spaces. For semisymmetric spaces in four dimensions with Lorentz signature, the Weyl tensor is easily seen (via spinors) to have a particularly simple quadratic property, which we call a special semisymmetric Weyl tensor. Using dimension...

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Bibliographic Details
Published in:Journal of physics. Conference series 2011-09, Vol.314 (1), p.012019-4
Main Authors: Edgar, S Brian, Senovilla, José M M
Format: Article
Language:English
Subjects:
Mathematical analysis
Physics
Signatures
Symmetry
Tensors
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Summary:Semisymmetric spaces are a natural generalisation of symmetric spaces. For semisymmetric spaces in four dimensions with Lorentz signature, the Weyl tensor is easily seen (via spinors) to have a particularly simple quadratic property, which we call a special semisymmetric Weyl tensor. Using dimensionally dependent tensor identities, all (conformally) semisymmetric spaces are confirmed to have special semisymmetric Weyl tensors for all signatures in four dimensions. Furthermore, all Ricci-semisymmetric spaces with special semisymmetric Weyl tensors are shown to be semisymmetric for all signatures in four dimensions. Counterexamples demonstrate that these two properties have no direct generalisations in higher dimensions.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/314/1/012019