{"paper":{"title":"Rigidity theorems of Lagrangian submanifolds in the homogeneous nearly K\\\"ahler $\\mathbb{S}^6(1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bangchao Yin, Jiabin Yin, Zejun Hu","submitted_at":"2019-02-05T11:13:20Z","abstract_excerpt":"In this paper, we study Lagrangian submanifolds of the homogeneous nearly K\\\"ahler $6$-dimensional unit sphere $\\mathbb{S}^6(1)$. As the main result, we derive a Simons' type integral inequality in terms of the second fundamental form for compact Lagrangian submanifolds of $\\mathbb{S}^6(1)$. Moreover, we show that the equality sign occurs if and only if the Lagrangian submanifold is either the totally geodesic $\\mathbb{S}^3(1)$ or the Dillen-Verstraelen-Vrancken's Berger sphere $S^3$ discribed in J Math Soc Japan, 42: 565-584, 1990."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01641","kind":"arxiv","version":2},"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"}