{
  "abstract": "For connected closed Lagrangian submanifolds of the homogeneous nearly Kähler sphere $\\mathbb S^6(1)$, we first establish a new integral inequality. Then, as applications we prove sharp pinching theorems for the scalar curvature $τ$ and Ricci curvature Ric, respectively: $τ\\ge \\tfrac{23}{8}$ implies either $τ=6$ with it totally geodesic, or $τ=\\tfrac{23}{8}$ with it congruent to the embedded Berger sphere of Dillen--Verstraelen--Vrancken; whereas ${\\rm Ric}\\geq\\frac18$ implies that the submanifold is either totally geodesic, or has constant sectional curvature $K=\\tfrac{1}{16}$, or is congruent to the embedded Berger sphere of Dillen-Verstraelen-Vrancken.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23470",
  "author_total": 3,
  "authors": [
    {
      "name": "Zejun Hu"
    },
    {
      "name": "Linlin Sun"
    },
    {
      "name": "Jiabin Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gvc6ex49bh7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23470",
  "fulltext_url": null,
  "id": "0gvc6ex49bh7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23470",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214029569",
  "pdf_url": "https://arxiv.org/pdf/2609.23470",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gvc6ex49bh7z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23470",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23470"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere",
  "title_text": "Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/0gvc6ex49bh7z",
  "venue": "arXiv",
  "versions": []
}