hey all,(adsbygoogle = window.adsbygoogle || []).push({});

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 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,

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Cartan's 1924 mystery formula ! differential Geometry

**Physics Forums | Science Articles, Homework Help, Discussion**