  In this paper we perform systematic investigation of all possible solutions
with static compact extra dimensions and expanding three-dimensional subspace
(``our Universe''). Unlike previous papers, we consider extra-dimensional
subspace to be constant-curvature manifold with both signs of spatial
curvature. We provide a scheme how to build solutions in all possible number of
extra dimensions and perform stability analysis for the solutions found. Our
study suggests that the solutions with negative spatial curvature of extra
dimensions are always stable while those with positive curvature are stable for
a narrow range of the parameters and the width of this range shrinks with
growth of the number of extra dimensions. This explains why in the previous
papers we detected compactification in the case of negative curvature but the
case of positive curvature remained undiscovered. Another interesting feature
which distinguish cases with positive and negative curvatures is that the
latter do not coexist with maximally-symmetric solutions (leading to
``geometric frustration'' of a sort) while the former could -- this difference
is noted and discussed.
