  Within the framework of the Einstein's standard equations of the general
theory of relativity, flat galactic rotational curves of galaxies cannot be
explained without hypothesis attracting the dark matter, the particles of which
had not yet been identified. The vacuum central-symmetric solution of the
equations of conformal gravitation is well known as metrics of
Mannheim-Kazanas, on the basis of which these curves receive purely geometrical
explanation. We show in our work that the metrics of Mannheim-Kazanas is the
solution of not only Bach equations received from conformal-invariant Weyl
Lagrangian, but also the solution of equations of the conformal
geometrodynamics at a nonzero vector of Weyl. In this connection the hypothesis
is formulated that the space on galactic scales can be described not only by
Riemannian geometry, but with geometry of Weyl.
