  Exact Newtonian potential with an extra space dimension compactified on a
circle is derived and studied. It is found that a point mass located at one
side of the circle can generate almost the same strength of gravitational force
at the other side. Combined with the brane-world scenarios, it means that
although one can not see a particle which is confined to another brane, one can
feel its gravity explicitly as if it were located on our brane. This leads to
the conclusion that matter on all branes may contribute equally to the
curvature of our brane. Therefore, dark matter is probably nothing unusual but
a `shadow' cast on our brane by hidden ordinary matter of other branes. It is
shown that the physical effect of this `shadow' could be modeled by a perfect
fluid with an effective mass density and a non-zero pressure. This fluid could
serve as a dark matter candidate with an equation of state p_{eff}=omega rho
_{eff} where omega is a positive r-dependent function and \omega \neq 0,1/3,\
implying that it is neither cold nor hot. So, if the higher-dimensional
universe contains several branes, the total amount of hidden matter would be
able to provide the required amount for dark matter. Meanwhile, dark matter
halos of galaxies might be just halos of the effective mass distribution
yielded by hidden ordinary stars, and these stars are confined on other branes
but captured by our galaxies. Some more properties and implications are also
discussed.
