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Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer inMaxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannianspace - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock -Ivanenko. In this approach, the Maxwell equations are solved exactly on thebackground of static cosmological Einstein model, parameterized by specialcylindrical coordinates and realized as a Riemann space of constant positivecurvature. A discrete frequency spectrum for electromagnetic modes depending onthe curvature radius of space and three parameters is found, and correspondingbasis electromagnetic solutions have been constructed explicitly. In the caseof elliptical model a part of the constructed solutions should be rejected bycontinuity considerations. Similar treatment is given for Maxwell equations inhyperbolic Lobachevsky model, the complete basis of electromagnetic solutionsin corresponding cylindrical coordinates has been constructed as well, noquantization of frequencies of electromagnetic modes arises.

Maxwell Equations in Complex Form of Majorana - Oppenheimer, Solutions with Cylindric Symmetry in Riemann S_{3} and Lobachevsky H_{3} Spaces