= Curvature form
{title2=$F(A)$}
{wiki}
= Curvature form of a connection
{synonym}
= Vector-bundle curvature
{synonym}
= Curvature matrix
{synonym}
The <curvature form> of a <connection on a vector bundle> is $F=dA+A\wedge A$ in a local frame. A <principal connection> has the corresponding <Lie algebra>-valued form $F=dA+\tfrac12[A\wedge A]$. It measures the failure of horizontal directions to be integrable.
The curvature is $F(A)=d_A^2$ and in a local frame satisfies $F(A)=dA+A\wedge A$.
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