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by identifications and isomorphisms. This theory is developped in a completely basis-free way in terms of projectors and is totally compatible with the pseudo-orthogonal groups plus dilatations, see
Tilgner in J. Math. Phys. 19 (1978) p. 1118-1125 and Tilgner Lect. Notes in Math. 1156 (1984) p. 316-339. Note that in quantum mechanics the relation between projectors and subspaces is well-known, especially in the statistical formulation of entropy. Why not in relativity? With a Weyl- and an Einstein-projector and a direct othogonal decomposision into three subspaces, the meaning of which being described by Singer & Thorpe's main theorem? Note that there is a symplectic analogon of this theory, giving rise to a graded generalization of both - use the Knowledge search for Roger Howe to read a PDF-version of his comments on "elegance" in "Remarks on Classical Invarint Theory" in Trans. Amer. Math. Soc. 313 (1989) p. 539-570. In addition there is a connection between such Curvature Structures and Clifford algebras, this being used by Petrov for classification.
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Following the elegant developments of Singer & Thorpe, Nomizu, Kulkarni and
Kowalski there should be a section having this title, since taking the three algebraic axioms alone (skew symmetry, Lie algebra property and first Bianchi-identity) there are no tensors in this business. They come in only
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There is a bit of confusion at the beginning of the article, I think the author wanted to say ricci tensor instead of
Riemann. Weyl tensor is part of reinmann tensor, so statements like Riemann tensor is like this while weyl tensor is like that does not make sense. Can someone authorize me to make
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The tensorial expression of the Weyl tensor is incorrect. There are two factors 2 missing in the last two terms. Recall that $ T_{}=\frac{1}{2}$ .
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The standard symbol for the Weyl tensor appears to be
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