{
  "abstract": "We study a one-parameter family of SO(4)-invariant pluriclosed Hermitian metrics $g_c$ with vanishing Bismut Ricci form on the affine quadric $Q_3\\cong TS^3$, previously described in the physics literature. For every real parameter $c$, we prove local existence and uniqueness of a real-analytic solution to the defining singular initial-value problem, together with positivity of the associated metric near the singular orbit $S^3$. We then establish global existence and completeness for $|c|\\leq1$ and finite-time degeneration for $|c|>1$. The complete family exhausts all SO(4)-invariant Bismut Hermitian-Einstein metrics on the affine quadric $Q_3$, and joins Stenzel's Kähler Ricci-flat to a metric that was first considered by Chamseddine-Volkov/Maldacena-Nuñez. We also determine the leading asymptotics and derive an explicit scalar curvature formula, proving strict positivity for the non-Kähler members and identifying the change in asymptotic scalar curvature at the endpoint $c=1$. Finally, we show that all these metrics are not Bismut flat and have full Bismut holonomy SU(3), providing new examples of such manifolds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27979",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabio Podestà"
    },
    {
      "name": "Alberto Raffero"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sw75hn0yrw5f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27979",
  "fulltext_url": null,
  "id": "0sw75hn0yrw5f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27979",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214158072",
  "pdf_url": "https://arxiv.org/pdf/2609.27979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sw75hn0yrw5f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Complete pluriclosed metrics with vanishing Bismut Ricci form on the affine quadric",
  "title_text": "Complete pluriclosed metrics with vanishing Bismut Ricci form on the affine quadric",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0sw75hn0yrw5f",
  "venue": "arXiv",
  "versions": []
}