  Let $Y$ be a closed Calabi-Yau manifold. Let $\omega$ be the K\"ahler form of
a Ricci-flat K\"ahler metric on $\mathbb{C}^m \times Y$. We prove that if
$\omega$ is uniformly bounded above and below by constant multiples of
$\omega_{\mathbb{C}^m} + \omega_Y$, where $\omega_{\mathbb{C}^m}$ is the
standard flat K\"ahler form on $\mathbb{C}^m$ and $\omega_Y$ is any K\"ahler
form on $Y$, then $\omega$ is actually equal to a product K\"ahler form, up to
a certain automorphism of $\mathbb{C}^m \times Y$.
