{"paper":{"title":"Compact locally conformal K\\\"ahler manifolds with constant Chern holomorphic sectional curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Xueyuan Wan, Zhuzhu Huang","submitted_at":"2026-06-23T11:04:05Z","abstract_excerpt":"We prove the Chern version of the constant holomorphic sectional curvature conjecture for compact locally conformal K\\\"ahler manifolds. More precisely, let $(M^n,h)$, $n\\geq2$, be a compact locally conformal K\\\"ahler manifold whose Chern holomorphic sectional curvature is a constant $c$. We show that $h$ is necessarily K\\\"ahler and therefore is a complex space form metric of holomorphic sectional curvature $c$. In particular, when $c=0$, the metric is K\\\"ahler flat. This removes the nonpositivity assumption from a theorem of Chen, Chen, and Nie. The proof derives a curvature identity on the un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24425","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/2606.24425/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"}