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Suppose we are given data for an electromagnetic potential $(\phi, A_1, A_2, A_3)$.  Suppose $M$ is a hypersurface of $S^4(1/h)$ with coordinates $(x^0, x^1, x^2, x^3)$ with $x^0$ normal to the surface and the rest tangent.  Consider the 1-form $A = \phi dx^0 + A_1 dx^1 + A_2 dx^2 + A_3 dx^3$.  We are interested in the self-duality equation $dA = *dA$.  Time does not enter as a variable, so this is not quite directly linked to the physical Maxwell’s equation but it is still worth studying as an attempt to understand how the peculiarities of four-dimensional geometry enter in the description of electromagnetism.  The usual account of Maxwell’s equations in differential forms can be seen in  YangMillsFromMaxwells.
Note that the electromagnetic field strength form, under the Hodge star operator sends $E$ to $-B$ and $B$ to $+E$, and although usual formulation will put $x^0$ to time, the behavior is the same with a space variable.  It is a space variable that produces the geometric interpretation for this duality of electric and magnetic fields via the star operator.