{"paper":{"title":"On the Motion of a Free Particle in the de Sitter Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Samuel A. Wainer, Waldyr A. Rodrigues Jr.","submitted_at":"2016-01-21T18:51:37Z","abstract_excerpt":"Let $M=SO(1,4)/SO(1,3)\\simeq S^{3}\\times\\mathbb{R}$ (a parallelizable manifold) be a submanifold in the structure $(\\mathring{M}% ,\\boldsymbol{\\mathring{g}})$ (hereafter called the bulk) where $\\mathring {M}\\simeq\\mathbb{R}^{5}$ and $\\boldsymbol{\\mathring{g}}$ is a pseudo Euclidian metric of signature $(1,4)$. Let $\\boldsymbol{i}:M\\rightarrow\\mathbb{R}^{5}$ be the inclusion map and let \\ $\\boldsymbol{g}=\\boldsymbol{i}^{\\ast }\\boldsymbol{\\mathring{g}}$ be the pullback metric on $M$. It has signature $(1,3)$ Let $\\boldsymbol{D}$ be the Levi-Civita connection of $\\boldsymbol{g}% $. We call the st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05751","kind":"arxiv","version":1},"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"}