{"paper":{"title":"Non-singular solutions to the normalized Ricci flow equation","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Fuquan Fang, Yuguang Zhang, Zhenlei Zhang","submitted_at":"2006-09-09T12:32:26Z","abstract_excerpt":"In this paper we study non-singular solutions of Ricci flow on a closed manifold of dimension at least 4. Amongst others we prove that, if M is a closed 4-manifold on which the normalized Ricci flow exists for all time t>0 with uniformly bounded sectional curvature, then the Euler characteristic $\\chi (M)\\ge 0$. Moreover, the 4-manifold satisfies one of the following \\noindent (i) M is a shrinking Ricci solition;\n  \\noindent (ii) M admits a positive rank F-structure;\n  \\noindent (iii) the Hitchin-Thorpe type inequality holds 2\\chi (M)\\ge 3|\\tau(M)| where $\\chi (M)$ (resp. $\\tau(M)$) is the Eul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609254","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0609254/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}