Talk:Ricci decomposition

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[edit] The term "Ricci decomposition"

I've recently seen this referred to by another name in papers on the arXiv. I am trying to find them again so that I can mention the alternative name. However, I believe the one I have given here is not only more accurate but is fairly standard in the mathematical literature--- I am also trying to locate the textbook(s) where I have seen it called by this name.---CH (talk) 19:12, 13 August 2005 (UTC)


Shouldn't

E_{abcd} = \frac{1}{n-2} \, \left( g_{ad} \, R_{bc} - g_{ac} \, R_{bd} + g_{bc} \, R_{ad} - g_{bd} \, R_{ac} \right)

read

E_{abcd} = \frac{1}{n-2} \, \left( g_{ad} \, S_{bc} - g_{ac} \, S_{bd} + g_{bc} \, S_{ad} - g_{bd} \, S_{ac} \right)

so that it really is constructed from S?

[edit] Terminology

During my time studying symmetries and working with the decomposition (I'm not giving 'the decomposition' a name yet), I was taught that:

\, S_{ab} was called the Trace-free Ricci tensor and usually denoted by \, \tilde{R}_{ab}.
\, E_{abcd} was referred to simply as the E-tensor (as did others who classified it - I forget the names, but I can find out).
The tensor \, H_{abcd} denoted by \, G_{abcd} and was sometimes called the G-tensor, but usually thought of as - and called - the bivector metric, as it behaves precisely like a metric on the space of bivectors.
The decomposition we often called the Géhéniau-Debever decomposition.

(At least) some of the above alternative terminologies are used in many research papers (certainly the trace-free Ricci tensor).

Well, I just seem to have complicated the whole issue of terminology in this article now! This may not be such a huge problem, and actually quite interesting, as the decomposition can obviously be defined mathematically (with it's own mathematical terminology) and it's applications to GR give alternative terminology. MP (talk) 11:00, 29 January 2006 (UTC)

[edit] Students beware

I extensively edited the August 2005 version of this article and had been monitoring it for bad edits, but I am leaving the WP and am now abandoning this article to its fate.

Just wanted to provide notice that I am only responsible (in part) for the last version I edited; see User:Hillman/Archive. I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.

Good luck to User:Mpatel and to all students searching for information, regardless!---CH 03:27, 1 July 2006 (UTC)

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