Geometric interpretation of the tensor of an electromagnetic field with orthogonal components E and B

An electromagnetic field with (B, E) = 0 is interpreted geometrically as associating with each point (x, y, z, t) of the projective line ℙ3. For this field, the general solution to the first four Maxwell equations, ℜ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{o}\mathfrak{t} $$\end{document}F = 0, is obtained. The remaining four equations are reduced, in a field with no charges and currents, to a problem which is bound up with the scalar wave equation.