Let $\pi: P \to M$ be a smooth principal right $G$-bundle, where $G$ is a Lie group with Lie algebra $\mathfrak{g} = T_eG$. For each $A \in \mathfrak{g}$, let $A_P \in \mathfrak{X}(P)$ denote the fundamental vector field defined by the right action:
and sends a horizontal distribution $H$ to the connection form $\omega^H$ defined by vertical projection along $H$ and identification of vertical tangent vectors with fundamental vector fields.