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Then either $M$ is biholomorphi"},"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":"0707.3894","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-07-26T10:43:21Z","cross_cats_sorted":[],"title_canon_sha256":"172b37f51ffacfe0a841091b06d26dd8cd698d8668bbcbafdb9b58707475d06c","abstract_canon_sha256":"278d250411cb597716efff71713b8c9989ac722677fad871e1c4771731e5b21e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:52.085348Z","signature_b64":"Z5tAd3rS+wRfuXBqnyw/olnyUlIo8ie67X2RClJdsu7hvQ+xp6gv+bIidhnxD4/nXqc7P1F1fNnSCO0LVaKlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cca5a7c2edf433e51c4d799ccae57904d7e802554cc0eec9f2dedb33380f7ba","last_reissued_at":"2026-05-18T04:24:52.084872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:52.084872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Manifolds with nonnegative isotropic curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Harish Seshadri","submitted_at":"2007-07-26T10:43:21Z","abstract_excerpt":"We prove that if $(M^n,g)$, $n \\ge 4$, is a compact, orientable, locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold:\n  (i) $M$ admits a metric with positive isotropic curvature\n  (ii) $(M,g)$ is isometric to a locally symmetric space\n  (iii) $(M,g)$ is K\\\"ahler and biholomorphic to $\\C P^\\frac {n}{2}$.\n  (iv) $(M,g)$ is quaternionic-K\\\"ahler.\n  This is implied by the following result:\n  Let $(M^{2n},g)$ be a compact, locally irreducible K\\\"ahler manifold with nonnegative isotropic curvature. 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