Let $n\in\mathbb N$, let $(M,\omega)$ be a smooth symplectic manifold of dimension $2n$, let $H\in C^\infty(M;\mathbb R)$, and let $c\in\mathbb R$ be a regular value of $H$. Set
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\begin{align*}
\Sigma:=H^{-1}(c).
\end{align*}
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Suppose that $\Sigma$ is a contact-type hypersurface with respect to a Liouville vector field $Y\in\mathfrak X(U)$ on an open neighbourhood $U\subset M$ of $\Sigma$, meaning
Let $X_H\in\mathfrak X(M)$ be the Hamiltonian vector field determined by
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\begin{align*}
\omega(X_H,\cdot)=dH.
\end{align*}
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Then the smooth function $dH(Y)|_\Sigma:\Sigma\to\mathbb R$ is nowhere zero, and the Reeb vector field $R_\alpha\in\mathfrak X(\Sigma)$ satisfies, for every $x\in\Sigma$,