On the Sectional Curvature Along Central Configurations

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 $1/r^{\alpha}$ potential with $\alpha> 0$. We also obtain dynamical consequences of these curvature values for relative equilibrium solutions. These curvature methods work well for strong forces ($\alpha \geqslant 2$).