{"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. Then either $M$ is biholomorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3894","kind":"arxiv","version":4},"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"}