  In the present paper the gauge-invariant formalism is developed for
perturbations of the brane-world model in which our universe is realized as a
boundary of a higher-dimensional spacetime. For the background model in which
the bulk spacetime is $(n+m)$-dimensional and has the spatial symmetry
corresponding to the isometry group of a $n$-dimensional maximally symmetric
space, gauge-invariant equations are derived for perturbations of the bulk
spacetime. Further for the case corresponding to the brane-world model in which
$m=2$ and the brane is a boundary invariant under the spatial symmetry in the
unperturbed background, relations between the gauge-invariant variables
describing the bulk perturbations and those for brane perturbations are derived
from Israel's junction condition under the assumption of $\ZR_2$ symmetry. In
particular, for the case in which the bulk spacetime is a constant-curvature
spacetime, it is shown that the bulk perturbation equations reduce to a single
hyperbolic master equation for a master variable, and that the physical
condition on the gauge-invariant variable describing the intrinsic stress
perturbation of the brane yield a boundary condition for the master equation
through the junction condition. On the basis of this formalism it is pointed
out that it seems to be difficult to suppress brane perturbations corresponding
to massive excitations for a brane motion giving a realistic expanding universe
model.
