  Complex formalism of Riemann - Silberstein - Majorana - Oppenheimer in
Maxwell electrodynamics is extended to the case of arbitrary pseudo-Riemannian
space - time in accordance with the tetrad recipe of Tetrode - Weyl - Fock -
Ivanenko. In this approach, the Maxwell equations are solved exactly on the
background of simplest static cosmological models, spaces of constant curvature
of Riemann and Lobachevsky parameterized by spherical coordinates. Separation
of variables is realized in the basis of Schr\"odinger -- Pauli type,
description of angular dependence in electromagnetic complex 3-vectors is given
in terms of Wigner D-functions. In the case of compact Riemann model a discrete
frequency spectrum for electromagnetic modes depending on the curvature radius
of space and three discrete parameters is found. In the case of hyperbolic
Lobachevsky model no discrete spectrum for frequencies of electromagnetic modes
arises.
