Talk:Weyl tensor

Requested move

Weyl curvature → Weyl tensor

• • From WP:RFD: Weyl tensor should not be redirected to Weyl curvature because similar articles are named blah tensor and because Weyl tensor is more common in literature than Weyl curvature or even Conformal curvature ---CH 19:49, 24 December 2005 (UTC)

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Moved.  ALKIVAR™ 13:26, 31 December 2005 (UTC)

Discussion

The tensorial expression of the Weyl tensor is incorrect. There are two factors 2 missing in the last two terms. Recall that $T_{[\mu \nu]}=\frac{1}{2}[T_{\mu \nu}-T_{\nu \mu}]$. — Preceding unsigned comment added by 95.252.167.74 (talk) 16:58, 9 August 2014 (UTC)

From WP:RFD:

Weyl tensor should not be redirected to Weyl curvature because similar articles are named blah tensor and because Weyl tensor is more common in literature than Weyl curvature or even Conformal curvature ---CH 19:49, 24 December 2005 (UTC)

Comment. Don't mistate the facts. Riemann curvature tensor redirects to Curvature tensor, keeping curvature in the title (but not including the name which distinguished that from this one, called in the introduction "Weyl curvature tensor". Please address these points. Gene Nygaard 21:21, 30 December 2005 (UTC)

symmetric metric

Since the metric is symmetric by definition won't $g_{a[c}$ vanish? --Michael C. Price ^talk 01:05, 26 January 2008 (UTC)

I assume you're referring to the expression for the Weyl tensor; if it was $g_{[ac]}$, then yes, it would vanish, but that does not occur in the expression. You can't just look at $g_{a[c}$ in isolation (only 1 bracket!). Consult any text on tensor algebra or GR for elucidation. MP ^{(talk•contribs)} 07:53, 26 January 2008 (UTC)

True, I misread the expression. --Michael C. Price ^talk 13:00, 27 January 2008 (UTC)

pseudo-othogonal curvature structures

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 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 Wikipedia 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. — Preceding unsigned comment added by 194.94.224.254 (talk • contribs) 14:39, 8 June 2010 (UTC)

Change symbol W_abcd to C_abcd

The standard symbol for the Weyl tensor appears to be C_abcd rather than W_abcd. The first six books I looked at on this use the former; any objections to it being changed to C as being the more standard symbol? — Quondum 07:36, 11 October 2012 (UTC)

Reimann tensor vs weyl tensor

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 amendments petite (talk) 14:48, 7 February 2022 (UTC)