  Let M be a compact Riemannian manifold and E a Riemannian vector bundle on M.
We look for hypersurfaces of E with a prescribed vertical Gaussian curvature.
In trying to solve this problem fibre-wise, we loose the regularity of the
resulting solution. To unsure the smoothness of the solution, we construct it
as a radial graph over the unit sphere subbundle of E and prove its existence
by solving in this one a nonlinear partial differential equation of
Monge-Amp\`ere type.
