{"paper":{"title":"Lagrangian submanifolds in complex space forms satisfying an improved equality involving $\\delta(2,2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alicia Prieto-Mar\\'in, Bang-Yen Chen, Xianfeng Wang","submitted_at":"2013-07-15T14:45:18Z","abstract_excerpt":"It was proved in [8,9] that every Lagrangian submanifold $M$ of a complex space form $\\tilde M^{5}(4c)$ of constant holomorphic sectional curvature $4c$ satisfies the following optimal inequality: {align}\\tag{A}\\delta(2,2)\\leq \\text{\\small${25}{4}$} H^{2}+8c,{align} where $H^{2}$ is the squared mean curvature and $\\delta(2,2)$ is a $\\delta$-invariant on $M$ introduced by the first author. This optimal inequality improves a special case of an earlier inequality obtained in [B.-Y. Chen, Japan. J. Math. 26 (2000), 105-127].\n  The main purpose of this paper is to classify Lagrangian submanifolds o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3968","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"}