  A regular contact manifold is a manifold $M$ equipped with a globally defined
contact form $\eta$ such that the topological space $M/\mathcal{R}$ of orbits
(trajectories) of the Reeb vector field $\mathcal{R}$ of $\eta$ carries a
smooth manifold structure, so the canonical projection $p:M\to M/\mathcal{R}$
is a smooth fibration. We show that, under the additional assumption that
$\mathcal{R}$ is a complete vector field, this fibration is actually either an
$S^1$- or an $\mathbb{R}$-principal bundle. Moreover, there exists a unique
symplectic form $\omega$ on $M/\mathcal{R}$ such that
$p^*(\omega)=\mathrm{d}\eta$ which is $\rho$-integral in the $S^1$-bundle case,
where $\rho$ is the minimal period of the $S^1$-action, so the symplectic
manifold $(M/\mathcal{R},\omega)$ admits a prequantization. We do not assume
that $M$ is compact.
