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## Main Question or Discussion Point

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?).

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).

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).