  Let $\pi : \mathcal X \to S$ be a local universal family of compact
Ricci-flat K\"ahler manifolds over a smooth base $S$. The complexified K\"ahler
cones of each fiber of the family form a holomorphic fiber bundle $\mathcal K
\to S$. We show that there exists a natural hermitian metric $\omega$ on the
fiber product $\mathcal X \times_S \mathcal K$. We then discuss the example of
elliptic curves in some detail.
