Maxwell Equations in Homogeneous Spaces with Solvable Groups of Motions

Abstract

The classification of exact solutions of Maxwell vacuum equations for the case where the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G3(VII) was completed. All non-equivalent exact solutions of Maxwell vacuum equations for electromagnetic fields and spaces with such symmetry were obtained. The vectors of the canonical frame of a homogeneous space of type VII according to the Bianchi classification and the electromagnetic field potentials were found.

Keywords

• Maxwell equations
• Klein–Gordon–Fock equation
• algebra of symmetry operators
• theory of symmetry
• linear partial differential equations