= Local principal connection form
{title2=$A=s^*\mathcal A,\quad A'=g^{-1}Ag+g^{-1}dg$}
= Gauge potential of a principal connection
{synonym}
Pulling a <principal connection> back along a local section $s$ gives a Lie-algebra-valued one-form on the base. If the section changes to $sg$, the form has the displayed inhomogeneous transformation. Its <gauge curvature> $F=dA+A\wedge A$ transforms homogeneously as $F'=g^{-1}Fg$. The collection of such local forms encodes a global <principal connection> even when no single section exists globally.
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