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

An electromagnetic field with $(\vec{B},\vec{E})=0$ is interpreted geometrically as associating with each point $(x,y,z,t)$ of the projective line $\mathbb{P}^3$. For this field, the general solution to the first four Maxwell equations, ${\mathop{\mathfrak{Rot}}\nolimits F=0}$, 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.