# On the sectional curvature along central configurations

## TL;DR

This paper links the geometry of the Jacobi-Maupertuis metric, via sectional curvature, to planar central configurations in the N-body problem, revealing new insights especially for strong force potentials.

## Contribution

It provides a novel geometric characterization of central configurations using sectional curvature for general masses and potentials.

## Key findings

- Curvature characterization applies to general masses and potentials
- Dynamical implications for relative equilibrium solutions
- Effective for strong force potentials with α ≥ 2

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