{
  "abstract": "This paper is concerned with the study on Legendrian submanifolds with conformal Maslov form in the unit sphere $\\mathbb{S}^{2n+1}$, which admits a Sasakian structure $(φ,ξ,η,g)$ for $n\\ge2$. As the main result, we classify such submanifolds with constant sectional curvature, motivated by the classification result of the minimal Legendrian submanifolds with constant sectional curvature. Moreover, we prove that, for a closed Legendrian submanifold $M^n$ in $\\mathbb{S}^{2n+1}$ with conformal Maslov form, if its sectional curvature satisfies the pinching $0\\leq\\sec_g\\leq1$, then either $M^n$ is the totally geodesic Legendrian sphere with $\\sec_g=1$, or $M^n$ is a closed embedded weighted Clifford torus with $\\sec_g=0$. This extends the corresponding pinching theorem of Dillen--Vrancken (J Math Pures Appl 69:85--93 1990) from minimal Legendrian submanifolds to the conformal Maslov class under the same curvature bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14021",
  "author_total": 2,
  "authors": [
    {
      "name": "Yong Luo"
    },
    {
      "name": "Cheng Xing"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akncq6ka2rygq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14021",
  "fulltext_url": null,
  "id": "akncq6ka2rygq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14021",
  "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": "W7213254462",
  "pdf_url": "https://arxiv.org/pdf/2609.14021",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akncq6ka2rygq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14021",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14021"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Legendrian submanifolds in the unit sphere with conformal Maslov form and constant sectional curvature",
  "title_text": "Legendrian submanifolds in the unit sphere with conformal Maslov form and constant sectional curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/akncq6ka2rygq",
  "venue": "arXiv",
  "versions": []
}