Geodesic
On Maxwell's Equations with a Magnetic Monopole on Manifolds
Informatics and Automation, Mathematical physics and applications, Tome 306 (2019), pp. 52-55.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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I. V. Volovich; V. V. Kozlov. On Maxwell's Equations with a Magnetic Monopole on Manifolds. Informatics and Automation, Mathematical physics and applications, Tome 306 (2019), pp. 52-55. http://geodesic.mathdoc.fr/item/TRSPY_2019_306_a4/

[1] Darboux G., “Problème de mécaniqie”, Bull. sci. math. astron. Sér. 2, 2:1 (1878), 433–436

[2] Poincaré H., “Remarques sur une expérience de M. Birkeland”, C. r. Acad. sci., 123 (1896), 530–533

[3] Dirac P.A.M., “Quantised singularities in the electromagnetic field”, Proc. R. Soc. London A, 133 (1931), 60–72 | DOI

[4] McDonald K.T., Birkeland, Darboux and Poincaré: Motion of an electric charge in the field of a magnetic pole, E-print, Princeton Univ., Princeton, NJ, 2015 http://www.physics.princeton.edu/~mcdonald/examples/birkeland.pdf