  The higher-dimensional generalization of Randall-Sundrum approach with
additional positive curvature $n$-dimensional and Ricci-flat $m$-dimensional
compuct subspaces is considered in pure gravity theory with metric of
space-time and $(p+1)$-form potential as basic fields. Introduction of mass
term of $(p+1)$-form potential into the action of co-dimension one brane
permits to stabilize brane's position and hence to calculate the value of
Planck/electroweek scales ratio. There are no ad hoc too large or too small
parameters in the theory; calculated mass hierarchy strongly depends on
dimensionalities $m$, $n$ of additional subspaces and its observed large value
in 4 dimensions (i.e. for $p=3$) is received in particular in $D13$ ($m=1$,
$n=7$) or $D16$ ($m=2$, $n=9$) space-times.
