Cartan's 1924 mystery formula ! differential Geometry

1. Sep 25, 2012

zn5252

hey all,
in this book ;
https://www.amazon.com/Geometry-Riemannian-Spaces-Lie-Groups/dp/0915692341/ref=sr_1_1?ie=UTF8&qid=1348590926&sr=8-1&keywords=geometry+of+riemannian+++spaces++cartan
On page 178 ( which I attach a snapshot of it) Cartan had introduced a formula (see in the snapshot formula 6) without any proof ! it deals with the Riemann curvature tensor and bivectors.
Does someone know where does this formula come from please ? I believe this is equivalent to the way we write the electromagnetism tensor two-form :
F = 1/2 dxμ ^ dxσ Fμσ
This is somehow related to the formula used by John wheeler in the article : http://www.springerlink.com/content/y04t0w6xg064517q/
where we can see a snapshot of the page on which it was mentioned :
Thank you,
cheers,

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Last edited: Sep 25, 2012
2. Sep 30, 2012

zn5252

I think i found a twin version of it in MTW (Gravitation) page 281. See attached.
Damn was I blind ?

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