  We study the influence of anisotropy, treated as a dimensional crossover
between 1D and 3D system, on the topological instability induced by a
(self-consistent) uniaxial periodic potential. The mechanism on which the
instability is based involves the topological reconstruction of the Fermi
surface, from initially closed pockets to the surface with open Fermi sheets,
creating two peculiar points in the band dispersion - the saddle point and
elliptical point, between which the pseudogap in electron density of states
develops. The self-consistent periodic potential appears as a result of
interactions, either electron-phonon, or electron electron, which, linked with
the topological instability of the system, results in formation of a new ground
state of the system - the density wave provided that the relevant coupling
constant is larger than critical. Our analysis shows that the phase transition
takes place along the whole continuous interval of a dimensional crossover
between 1D and 3D, but that the critical coupling strength significantly
increases with the dimensionality of the system. It is our intention to give an
initial framework for understanding the nature of charge density waves
experimentally observed in a number of materials, like high$-T_c$ cuprates or
graphite intercalates, both being materials with a closed, rather isotropic
Fermi surface far from the nesting regime.
