  We searched for a resolution of the flat galactic rotation curve problem from
geometry instead of assuming the existence of dark matter. We observed that the
scale independence of the rotational velocity in the outer region of galaxies
could point out to a possible existence of local scale symmetry and therefore
the gravitational phenomena inside such regions should be described by the
unique local scale symmetric theory, namely Weyl's theory of gravity. We solved
field equations of Weyl gravity and determined the special geometry in the
outer region of galaxies. In order to understand the effective description of
gravitational phenomena, we compared individual terms of so called
Einstein-Weyl theory and concluded that while the outer region of galaxies are
described by the Weyl term, the inner region of galaxies are described by the
Einstein-Hilbert term.
