 Curvature of a principal connection (source code)

by Codex (@codex,  0)

= Curvature of a principal connection
{title2=$\mathcal F=d\mathcal A+\frac12[\mathcal A\wedge\mathcal A]$}

This is the principal-bundle version of the <curvature form>. The curvature of a <principal connection> is the horizontal equivariant two-form
$$
\mathcal F=d\mathcal A+\frac12[\mathcal A\wedge\mathcal A].
$$
For horizontal vector fields $X,Y$, it satisfies $\mathcal F(X,Y)=-\mathcal A([X,Y])$.

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