  On the base of an exact solution for the static spherically symmetric
Einstein equations with the quintessential dark matter, we explain the
asymptotic behavior of rotation curves in spiral galaxies. The parameter of the
quintessence state, i.e. the ratio of its pressure to the density is tending to
-1/3. We present an opportunity to imitate the relevant quintessence by
appropriate scalar fields in the space-time with extra 2 dimensions.
