Three dimensional central configurations in H3 and S3

Abstract

We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere. However, there exist both special and ordinary central configurations in the three-dimensional sphere that are not confined to any two-dimensional sphere.

10 pages, 2 figures

References in corpus (3)

• Bifurcations of the Lagrangian orbits from the classical to the curved 3-body problem
• Central configurations of the curved $N$-body problem
• Stability of fixed points and associated relative equilibria of the $3$-body problem on ${\mathbb{S}}^1$ and ${\mathbb{S}}^2$

Cited by in corpus (1)

• Equal masses results for choreographies $n$-body problems