{
  "abstract": "Nearly $\\mathrm{G}_2$ manifolds are positive Einstein seven-dimensional manifolds whose associated cone metric has special holonomy equal to, or contained in, $\\mathrm{Spin}(7)$. We study nearly parallel $\\mathrm{G}_2$-structures invariant under a cohomogeneity-one action of $\\mathrm{SO}(4)$, and construct the first inhomogeneous nearly parallel $\\mathrm{G}_2$-structure on the Berger space $\\mathrm{SO}(5)/\\mathrm{SO}(3)$. The cone over this metric has full holonomy $\\mathrm{Spin}(7)$. The existence of the solution is established by a rigorous computer-assisted shooting argument. We also establish a local desingularisation of a finite quotient of the sine cone over $S^3\\times S^3$ by gluing in the asymptotically conical $C_7$ bubble constructed by Foscolo--Haskins--Nordström. We show that as the singular orbit of a family of nearly parallel $\\mathrm{G}_2$ manifolds collapses, away from the singular orbit the desingularising family converges to the sine cone quotient, while the natural blow-up converges to the AC torsion-free $\\mathrm{G}_2$-metric of $C_7$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37265",
  "author_total": 2,
  "authors": [
    {
      "name": "Simon Salamon"
    },
    {
      "name": "Ragini Singhal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/14x3qspdk5vs3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37265",
  "fulltext_url": null,
  "id": "14x3qspdk5vs3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37265",
  "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": "W7221354465",
  "pdf_url": "https://arxiv.org/pdf/2609.37265",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/14x3qspdk5vs3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37265"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "New Inhomogeneous Nearly $\\mathrm{G}_2$-metric on the Berger Space and a Sine Cone Desingularisation",
  "title_text": "New Inhomogeneous Nearly G_2-metric on the Berger Space and a Sine Cone Desingularisation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/14x3qspdk5vs3",
  "venue": "arXiv",
  "versions": []
}