  Any connection between dark matter and extra dimensions can be cognizably
evinced from the associated effective energy-momentum tensor. In order to
investigate and test such relationship, a higher dimensional spacetime endowed
with a factorizable general metric is regarded to derive a general expression
for the stress tensor -- from the Einstein-Hilbert action -- and to elicit the
effective gravitational potential. A particular construction for the case of
six dimensions is provided, and it is forthwith revealed that the missing mass
phenomenon may be explained, irrespective of the dark matter existence.
Moreover, the existence of extra dimensions in the universe accrues the
possibility of a straightforward mechanism for such explanation. A
configuration which density profile coincides with the Newtonian potential for
spiral galaxies is constructed, from a 4-dimensional isotropic metric plus
extra-dimensional components. A Miyamoto-Nagai \emph{ansatz} is used to solve
Einstein equations. The stable rotation curves associated to such system are
computed, in full compliance to the observational data, without fitting
techniques. The density profiles are reconstructed and compared to that ones
obtained from the Newtonian potential.
