Classification of positive elliptic-elliptic rotopulsators on Clifford tori

Abstract

We prove that positive elliptic-elliptic rotopulsator solutions of the $n$-body problem in spaces of constant Gaussian curvature that move on Clifford tori of nonconstant size either lie on great circles, or project onto regular polygons. We additionally prove for the case that the configurations project onto regular polygons that all masses are equal and show that all these different types of positive elliptic-elliptic rotopulsator exist.