  K\"ahler-Einstein metrics for polarized families of Calabi-Yau manifolds
define a natural hermitian metric on the relative canonical bundle. The fact
that the curvature form is equal to the pull-back of the Weil-Petersson form up
to a numerical constant is being used for the construction of a K\"ahler form
on the total space of a given family, whose restriction to the fibers is Ricci
flat.
