{
  "abstract": "Let $M^n$ be a closed simply connected Legendrian submanifold of $\\mathbb S^{2n+1}$, where $n\\geq5$, and let $\\mathbf{B}$ and $\\mathbf{H}=\\operatorname{tr}\\mathbf{B}$ denote its second fundamental form and mean-curvature vector. We prove that $M$ is homeomorphic to $\\mathbb S^n$ if \\begin{equation*} |\\mathbf{B}|^2\\leq \\frac{(n-1)(n+2)}n+\\frac{n^2+3n-2}{2n^2}|\\mathbf{H}|^2-\\frac{(n-1)(n-2)}{2n^2}|\\mathbf{H}|\\sqrt{|\\mathbf{H}|^2+4n}. \\end{equation*} The equality can be attained by the Calabi products, so simple connectivity cannot be omitted. For $n\\geq4$, we also prove a sphere theorem under an explicit bound and the weaker assumption $b_1(M;\\mathbb R)=0$. The proof combines phase-rotated Lawson--Simons variations with a systolic inequality for finite two-complexes. We also give local constructions showing that the pinching condition allows negative isotropic curvature at a point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18293",
  "author_total": 2,
  "authors": [
    {
      "name": "Qing Cui"
    },
    {
      "name": "Linlin Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/68t9pqhvx5203.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18293",
  "fulltext_url": null,
  "id": "68t9pqhvx5203",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18293",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221777720",
  "pdf_url": "https://arxiv.org/pdf/2610.18293",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/68t9pqhvx5203.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18293",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18293"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A topological sphere theorem for pinched Legendrian submanifolds",
  "title_text": "A topological sphere theorem for pinched Legendrian submanifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/68t9pqhvx5203",
  "venue": "arXiv",
  "versions": []
}