  Motion of a classical particle in 3-dimensional Lobachevsky and Riemann
spaces is studied in the presence of an external magnetic field which is
analogous to a constant uniform magnetic field in Euclidean space. In both
cases three integrals of motions are constructed and equations of motion are
solved exactly in the special cylindrical coordinates on the base of the method
of separation of variables. In Lobachevsky space there exist trajectories of
two types, finite and infinite in radial variable, in Riemann space all motions
are finite and periodical. The invariance of the uniform magnetic field in
tensor description and gauge invariance of corresponding 4-potential
description is demonstrated explicitly. The role of the symmetry is clarified
in classification of all possible solutions, based on the geometric symmetry
group, SO(3,1) and SO(4) respectively.
