{
  "abstract": "We construct an explicit deformation of the bi-invariant metric on Sp(2) whose induced metrics on the Gromoll-Meyer exotic 7-sphere have positive sectional curvature for all sufficiently small positive parameters. The deformation is determined by a fixed self-adjoint operator compatible with the quotient action. The proof combines a uniform curvature estimate with an algebraic analysis of the horizontal commuting planes. On the critical set where the lower-order positive terms vanish, we establish an explicit positive lower bound for the cubic coefficient of the curvature numerator. Uniform control of the fourth-order remainder and a compactness argument then show that every sectional curvature is positive",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11484",
  "author_total": 1,
  "authors": [
    {
      "name": "Zexuan Ouyang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ra946vk9jx0s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11484",
  "fulltext_url": null,
  "id": "5ra946vk9jx0s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11484",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7212319814",
  "pdf_url": "https://arxiv.org/pdf/2609.11484",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ra946vk9jx0s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11484",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11484"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A positively curved metric on the Gromoll-Meyer sphere",
  "title_text": "A positively curved metric on the Gromoll-Meyer sphere",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/5ra946vk9jx0s",
  "venue": "arXiv",
  "versions": []
}