On the Sectional Curvature Along Central Configurations

Abstract

In this paper we characterize planar central configurations in terms of a sectional curvature value of the Jacobi–Maupertuis metric. This characterization works for the N-body problem with general masses and any 1/r^α potential with α > 0. We also obtain dynamical consequences of these curvature values for relative equilibrium solutions. These curvature methods work well for strong forces (α ≥ 2).