We study some geometrical and topological properties of the electric fields created by point charges on Riemannian manifolds. Particularly, we characterize the spaces on which the electric lines emanating from a point charge are geodesics, and describe the topological properties of the basin boundary for $N$ point charges. Several open problems will be posed.
"Electric Fields Created by Point Charges: Some Geometrical and Topological Results." J. Geom. Symmetry Phys. 5 14 - 23, 2006. https://doi.org/10.7546/jgsp-5-2006-14-23