  The observed excess of gravitational forces in galaxies and galactic clusters
is usually referred as the existence of "dark matter particles" of unknown
origin. An alternative explanation of the dark matter effect is presented here
by assuming that the empty space of the Universe has a complicated geometrical
structure. It is assumed that the cosmological Lambda term, which is
approximately constant at scales of several Mpc and describes the dark energy,
is not constant at scales of several tenth of Kpc and describes the "dark
matter effect". This term is mathematically analogous, but not identical, with
the energy-momentum tensor of particles ensembles. In this connection the
general expression of the Riemann tensor, which depends on the matter
distribution in space and on the empty space geometry, is considered. The Ricci
tensor does not describe all possible empty space structures. The tensor of the
spin curvature also has to be taken into account. Local deviations of the empty
space geometry of Universe from a flat one provide the same observational
effect as clouds of invisible particles which demonstrate themselves by their
gravitational fields only. The matter, which forms stars and galaxies, will
concentrate in gravitational depressions of empty space. The gravitation
provides correlation of the luminous matter distribution and geometrical
structures of space. The presented theory is compared with observations.
