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Motion of a classical particle in 3-dimensional Lobachevsky and Riemannspaces is studied in the presence of an external magnetic field which isanalogous to a constant uniform magnetic field in Euclidean space. In bothcases three integrals of motions are constructed and equations of motion aresolved exactly in the special cylindrical coordinates on the base of the methodof separation of variables. In Lobachevsky space there exist trajectories oftwo types, finite and infinite in radial variable, in Riemann space all motionsare finite and periodical. The invariance of the uniform magnetic field intensor description and gauge invariance of corresponding 4-potentialdescription is demonstrated explicitly. The role of the symmetry is clarifiedin classification of all possible solutions, based on the geometric symmetrygroup, SO(3,1) and SO(4) respectively.

Classical Particle in Presence of Magnetic Field, Hyperbolic Lobachevsky and Spherical Riemann Models