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Cartan's 1924 mystery formula ! differential Geometry

  1. Sep 25, 2012 #1
    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,
     

    Attached Files:

    Last edited: Sep 25, 2012
  2. jcsd
  3. Sep 30, 2012 #2
    I think i found a twin version of it in MTW (Gravitation) page 281. See attached.
    Damn was I blind ?
     

    Attached Files:

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