On Maxwell's Equations with a Magnetic Monopole on Manifolds

We consider a generalization of Maxwell's equations on a pseudo-Riemannian manifold $M$ of arbitrary dimension in the presence of electric and magnetic charges and prove that if the cohomology groups $H^2(M)$ and $H^3(M)$ are trivial, then solving these equations reduces to solving the d'Alembert–Hodge equation.