{"paper":{"title":"Global properties of tight Reeb flows with applications to Finsler geodesic flows on $S^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Pedro A. S. Salom\\~ao, Umberto Hryniewicz","submitted_at":"2011-02-07T23:46:16Z","abstract_excerpt":"We show that if a Finsler metric on $S^2$ with reversibility $r$ has flag curvatures $K$ satisfying $(\\frac{r}{r+1})^2 <K \\leq 1$, then closed geodesics with specific contact-topological properties cannot exist, in particular there are no closed geodesics with precisely one transverse self-intersection point. This is a special case of a more general phenomenon, and other closed geodesics with many self-intersections are also excluded. We provide examples of Randers type, obtained by suitably modifying the metrics constructed by Katok \\cite{katok}, proving that this pinching condition is sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1474","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"}