{"paper":{"title":"Closed geodesics on positively curved spheres $S^n$ with Finsler metric induced by $(\\mathbb{R}P^n,F)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.DG","authors_text":"Hui Liu, Wei Wang","submitted_at":"2018-04-17T12:21:11Z","abstract_excerpt":"It's well known that the n-sphere $S^n$ is the universal double covering of the $n$-dimensional real projective space $\\mathbb{R}P^n$ and then any Finsler metric on $\\mathbb{R}P^n$ induces a Finsler metric of $S^n$. In this paper, we prove that for every Finsler $(S^n, F)$ for $n\\geq3$ whose metric is induced by irreversible Finsler $(\\mathbb{R}P^n,F)$ with reversibility $\\lambda$ and flag curvature $K$ satisfying $(\\frac{\\lambda}{\\lambda+1})^2<K\\leq 1$, there exist at least $n-1$ prime closed geodesics on $(S^n, F)$. Furthermore, if there exist finitely many distinct closed geodesics on $(S^n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06193","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"}