Möbius solutions of the curved $n$--body problem for positive curvature

Abstract

We denote by ${\mathbb{M}}_R^2$ a two dimensional space of constant positive Gaussian curvature. With methods of Möbius geometry and using the classification of the Möbius group of automorphisms ${\mathbf{Mob}}_2(\hat{\mathbb{C}})$ of the Riemman sphere $\hat{\mathbb{C}}={\mathbb{M}}_R^2\cup \{\infty \}$, we give algebraic conditions for the existence of Möbius solutions on $\hat{\mathbb{C}}$, getting a complete classification of them. We show several families of this kind of solutions.

33 pages, 4 figures

References in corpus (2)

• An intrinsic approach in the curved n-body problem: the negative curvature case
• Relative equilibria in the 3-dimensional curved n-body problem

Cited by in corpus (2)

• On certain Möbius type solutions for the n-body problem in a positive space form
• The Vlasov-Poisson equation, the Moebius Geometry and then-body problem in a negative space form