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arXiv · 1207.0737

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

Ernesto Perez-Chavela·J. Guadalupe Reyes-Victoria
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Abstract

We denote by $\mathbb{M}^2_R$ a two dimensional space of constant positive Gaussian curvature. With methods of Möbius geometry and using the classification of the Möbius group of automorphisms ${\rm \bf Mob}_2 \, (\hat{\mathbb{C}})$ 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.

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Ernesto Perez-Chavela, J. Guadalupe Reyes-Victoria. 2012-08-22. Möbius solutions of the curved $n$--body problem for positive curvature. https://arxiv.org/abs/1207.0737

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