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$$d F = 0; \ \ d \star F = 0.$$

And in the theory of gauge fields, one can introduce a connection one-from A from which one can formulate general Maxwell equations (for Yang-Mills fields) by

$$ dF + A \wedge F = 0; \ \ d \star F + A \wedge \star F = 0,$$

or if one introduces the covariant exterior derivative, just

$$D F = 0; \ \ D\star F = 0.$$

Is it also possible to introduce a curved-space covariant exterior derivative and express the curved-space Maxwell equations in terms of this? If so I would very much appreciate some links to literature where I could read about it.