Why is the definition of the curvature form for a Cartan connection the correct definition, and what does it actually tell you? I've read that it "measures the failure of the structural equation" but I suppose I don't really understand the structural equation (of a Maurer-Cartan form) anyway, and also how exactly does it measure the failure (obviously it's zero if it holds, but apart from that?).(adsbygoogle = window.adsbygoogle || []).push({});

If it would be necessary to go via an explanation of the Riemannian curvature tensor, I would also like to understand that (bearing in mind I have studied very little Riemannian geometry).

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# Curvature form of Cartan connections

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