{
  "abstract": "Let $X:M^3\\to\\R^4$ be a complete, connected self-shrinker without boundary, and suppose that the squared norm $S$ of its second fundamental form is constant. We prove that $S=0$ or $S=1$. Accordingly, the image is a hyperplane through the origin or a generalized cylinder $\\mathbb S^k(\\sqrt{k})\\times\\R^{3-k}$, $1\\le k\\le3$, and the immersion is a Riemannian covering onto its image.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18947",
  "author_total": 2,
  "authors": [
    {
      "name": "Shanlin Guan"
    },
    {
      "name": "Yuhang Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0xx9af6nscsma.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18947",
  "fulltext_url": null,
  "id": "0xx9af6nscsma",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18947",
  "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": "W7222226215",
  "pdf_url": "https://arxiv.org/pdf/2610.18947",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0xx9af6nscsma.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.18947",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18947"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rigidity of Three-Dimensional Self-Shrinkers with Constant Norm of the Second Fundamental Form",
  "title_text": "Rigidity of Three-Dimensional Self-Shrinkers with Constant Norm of the Second Fundamental Form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/0xx9af6nscsma",
  "venue": "arXiv",
  "versions": []
}