{
  "abstract": "This note gives direct proofs that, under an effective isometric $T^2$ action, Einstein metrics on smooth homotopy four-spheres are round and complete Ricci-flat metrics on smooth manifolds homeomorphic to $\\mathbb R^4$ are Euclidean or positive one-center Taub--NUT, up to isometry, scaling, and orientation reversal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12210",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiuxiong Chen"
    },
    {
      "name": "Conghan Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3ssy576v04v5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12210",
  "fulltext_url": null,
  "id": "a3ssy576v04v5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12210",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7221188954",
  "pdf_url": "https://arxiv.org/pdf/2610.12210",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3ssy576v04v5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.12210",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12210"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Einstein metrics with torus symmetry on $S^4$ and $\\mathbb R^4$",
  "title_text": "Einstein metrics with torus symmetry on S^4 and ℝ^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/a3ssy576v04v5",
  "venue": "arXiv",
  "versions": []
}