  Considering a separable and purely kinetic 5D scalar field on a warped
product metric background we propose a new and more general approach for
inducing 4D scalar potentials on a 4D constant foliation of the 5D space-time.
We obtain an induced potential for a true 4D scalar field instead of a
potential for an effective 4D scalar field. In this formalism we can recover
the usual 4D inflationary formalism with a geometrically induced inflationary
potential. In addition the quantum confinement of the inflaton modes is
obtained naturally from the model for at least a class of warping factors.
Besides the 4D inflationary physics that results of this formalism is
independent of the 4D-hypersurface chosen.
