Geometrical and topological aspects of Electrostatics on Riemannian manifolds

We study some geometrical and topological properties of the electric fields created by point charges on Riemannian manifolds from the viewpoint of the theory of dynamical systems. We provide a thorough description of the structure of the basin boundary and its connection with the topology of the manifold, and characterize the spaces in which the orbits of the electric field are geodesics. We also consider symmetries of electric fields on manifolds, particularly on spaces of constant curvature.