{
  "abstract": "The Landsberg Berwald conjecture asks whether every regular Landsberg metric is Berwald. We settle this conjecture for closed three-dimensional manifolds: every smooth strongly convex regular Landsberg metric on such a manifold is Berwald, without any reversibility assumption. Equivalently, there are no regular Landsberg \"unicorns\" on closed three-manifolds; this is a reformulation of the same conjecture, rather than a second independent conjecture.The proof combines a vanishing theorem for commuting Codazzi cubic tensors on closed surfaces, a rigidity theorem for three dimensional Minkowski norms with constant curvature indicatrices, and a rank one argument for the nonlinear curvature. The remaining R-quadratic case is settled by compactness along the geodesic flow. The fibrewise constant curvature theorem is an ingredient in this argument and does not assert the full Laugwitz conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11718",
  "author_total": 2,
  "authors": [
    {
      "name": "Jianyu Mao"
    },
    {
      "name": "Linfeng Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pbk246qs5tjm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11718",
  "fulltext_url": null,
  "id": "1pbk246qs5tjm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11718",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7212317323",
  "pdf_url": "https://arxiv.org/pdf/2609.11718",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pbk246qs5tjm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11718",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11718"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Rigidity of the closed three dimensional regular Landsberg metrics",
  "title_text": "The Rigidity of the closed three dimensional regular Landsberg metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/1pbk246qs5tjm",
  "venue": "arXiv",
  "versions": []
}