{"paper":{"title":"M\\\"obius solutions of the curved $n$--body problem for positive curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ernesto Perez-Chavela, J. Guadalupe Reyes-Victoria","submitted_at":"2012-07-03T16:14:10Z","abstract_excerpt":"We denote by $\\mathbb{M}^2_R$ a two dimensional space of constant positive Gaussian curvature. With methods of M\\\"obius geometry and using the classification of the M\\\"obius 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 M\\\"obius solutions on $\\hat{\\mathbb{C}}$, getting a complete classification of them. We show several families of this kind of solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0737","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}