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hey all,
in this book ;
https://www.amazon.com/GeometryRiemannianSpacesLieGroups/dp/0915692341/ref=sr_1_1?ie=UTF8&qid=1348590926&sr=81&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 twoform :
F = 1/2 dx^{μ} ^ dx^{σ} F_{μσ}
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,
in this book ;
https://www.amazon.com/GeometryRiemannianSpacesLieGroups/dp/0915692341/ref=sr_1_1?ie=UTF8&qid=1348590926&sr=81&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 twoform :
F = 1/2 dx^{μ} ^ dx^{σ} F_{μσ}
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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