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In this article, we show that $k=n-r$ where $r$ is the Ricci rank of the initial metric. As a corollary, we also confirm a splitting conjecture of Wu-Zheng when curvature is assumed to be bounded."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.2504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-12T15:26:43Z","cross_cats_sorted":[],"title_canon_sha256":"fcec1c6042cfd9ed16bd8e91089e7f59a803d28337ce8f16fdcf15f7f289a9ef","abstract_canon_sha256":"21dda81ddd4181e649a04551ed6d6aa6f8a07e0dcf544bbd2e812838786ad804"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:37.522819Z","signature_b64":"FeMVLyi6JIIaleye3+Jdz9NTi9gxzBFKgEhKlDFy6DCGPk9hP+v6FrERzeJvPYBxjYTCk60Fn4S2l8klvs0cAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87cf054085c23b9559e3a08f31d3f057a83ae6853733746f3a19682adfbfb745","last_reissued_at":"2026-05-18T04:13:37.521959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:37.521959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Wu-Zheng's Splitting Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chengjie Yu","submitted_at":"2011-09-12T15:26:43Z","abstract_excerpt":"Cao's splitting theorem says that for any complete K\\\"ahler-Ricci flow $(M,g(t))$ with $t\\in [0,T)$, $M$ simply connected and nonnegative bounded holomorphic bisectional curvature, $(M,g(t))$ is holomorphically isometric to $\\C^k\\times (N,h(t))$ where $(N,h(t))$ is a Kahler-Ricci flow with positive Ricci curvature for $t>0$. 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