Explicit solutions of Maxwell's equations on a space of constant curvature

An explicit solution is given to the Cauchy problem for the source-free Maxwell's equations in a vacuum on a space-time of the form $\text{R}$¹ X M₃, where M₃ is a 3-manifold of constant curvature. This solution satisfies Huyghens' Principle, that all electromagnetic radiation propagates at exactly the speed of light. The solution is obtained by harmonic analysis on M₃, and in the process a generating class of plane wave solutions is found. These solutions approximate the flat-space plane wave solutions in a neighbourhood of a point, but their global properties are somewhat different. The solutions obtained are easily transplanted to the Robertson-Walker models of General Relativity by re-scaling the time variable.