Talk:Cartan connection applications
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I fail to see how this article pertains to cartan connections. It might be better off in moving frame, or other such place. It is nearly the standard connection form formalism (not Cartan), presenting the exterior covariant derivative as the centerpiece, but with a lot of fanfare and excessive bold type. I'll see what I can do with it later, but I have my hands full now. Silly rabbit 20:15, 30 June 2006 (UTC)
- I agree, this article has very little to do with Cartan connections and should be renamed. There is a link, but it is somewhat indirect. This article is connected with the Einstein-Cartan theory of gravity, which is an extension of Einstein's theory of general relativity in which the Levi-Civita connection of the metric is replaced by a metric connection with torsion. This torsion is supposed to describe the coupling of spin to gravity. Underlying Cartan's idea, however, is the philosophy that one should not be working with an O(3,1) connection on the orthonormal frame bundle (equivalently, a metric linear connection), but a Cartan connection for the Poincare group. The torsion then appears as the translational component of the curvature of this connection. Unfortunately, the Einstein-Cartan article doesn't bring this out (indeed it seems to be mostly written by someone wishing to promote the theory to experts in general relativity rather than describe and explain it to a wider audience). Geometry guy 17:31, 14 February 2007 (UTC)
