  We investigate preheating in a higher-dimensional generalized Kaluza-Klein
theory with a quadratic inflaton potential $V(\phi)=\frac12 m^2\phi^2$
including metric perturbations explicitly. The system we consider is the
multi-field model where there exists a dilaton field $\sigma$ which corresponds
to the scale of compactifications and another scalar field $\chi$ coupled to
inflaton with the interaction $\frac12 g^2\phi^2\chi^2+\tilde{g}^2\phi^3\chi$.
In the case of $\tilde{g}=0$, we find that the perturbation of dilaton does not
undergo parametric amplification while the $\chi$ field fluctuation can be
enhanced in the usual manner by parametric resonance. In the presence of the
$\tilde{g}^2\phi^3\chi$ coupling, the dilaton fluctuation in sub-Hubble scales
is modestly amplified by the growth of metric perturbations for the large
coupling $\tilde{g}$. In super-Hubble scales, the enhancement of the dilaton
fluctuation as well as metric perturbations is weak, taking into account the
backreaction effect of created $\chi$ particles. We argue that not only is it
possible to predict the ordinary inflationary spectrum in large scales but
extra dimensions can be held static during preheating in our scenario.
