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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 simplest static cosmological models, spaces of constant curvatureof Riemann and Lobachevsky parameterized by spherical coordinates. Separationof variables is realized in the basis of Schr\"odinger -- Pauli type,description of angular dependence in electromagnetic complex 3-vectors is givenin terms of Wigner D-functions. In the case of compact Riemann model a discretefrequency spectrum for electromagnetic modes depending on the curvature radiusof space and three discrete parameters is found. In the case of hyperbolicLobachevsky model no discrete spectrum for frequencies of electromagnetic modesarises.

Maxwell Equations in Complex Form, Spherical Waves in Spaces of Constant Curvature of Lobachevsky and Riemann