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 ?³. For this field, the general solution to the first four Maxwell equations, ?\(\mathfrak{o}\mathfrak{t}\) 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.