{
  "abstract": "We prove that every compact connected positive quaternionic--Kähler manifold of real dimension $4n$ with $n\\ge2$ is isometric to a Wolf space after rescaling the metric by a positive constant. This proves the LeBrun--Salamon conjecture. The proof uses transverse rational curves and the contact structure of the twistor space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10410",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhengyu Hu"
    },
    {
      "name": "Kefeng Liu"
    },
    {
      "name": "Xueyuan Wan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5be35e2s064mw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10410",
  "fulltext_url": null,
  "id": "5be35e2s064mw",
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  "landing_url": "https://arxiv.org/abs/2610.10410",
  "language": null,
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  "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.AG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7221034779",
  "pdf_url": "https://arxiv.org/pdf/2610.10410",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5be35e2s064mw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10410",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10410"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Transverse rational curves and the LeBrun--Salamon conjecture",
  "title_text": "Transverse rational curves and the LeBrun--Salamon conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/5be35e2s064mw",
  "venue": "arXiv",
  "versions": []
}