{"paper":{"title":"Rigidity theorems of complete K\\\"ahler-Einstein manifolds and complex space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hezi Lin, Tian Chong, Yibin Ren, Yuxin Dong","submitted_at":"2014-09-12T11:27:33Z","abstract_excerpt":"We derive some elliptic differential inequalities from the Weitzenb\\\"ock formulas for the traceless Ricci tensor of a K\\\"ahler manifold with constant scalar curvature and the Bochner tensor of a K\\\"ahler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some $L^p$ and $L^\\infty $ pinching results are established to characterize K\\\"ahler-Einstein manifolds among K\\\"ahler manifolds with constant scalar curvature, and others are given to characterize complex space forms among K\\\"ahler-Einstein manifolds. Finally, these pinching results may be combined to characterize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3703","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":""},"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"}