{
  "abstract": "An admissible configuration $Λ\\subset\\Hh^m\\simeq\\Rr^{4m}$ defines a compact intersection of quadrics $Z_{\\Hh}(Λ)$ and a free diagonal $\\Sp(1)$ quotient $N_{\\Hh}(Λ)$. We realize this quotient as the leaf space of a real dilation action on an open subset of quaternionic projective space. The total space is a quaternionic moment-angle polyhedral product. Every quotient is $2$-connected; when there are no indispensable coordinates, it is $3$-connected and its fourth integral cohomology is generated by the Euler class $e$ of the associated oriented rank-four bundle. We compute $p_1(TN_{\\Hh})=2(n-2)e$ and prove that no LVMQ manifold admits a quaternionic Kähler metric. An explicit infinite family consists of products of spheres admitting both homogeneous positive Einstein metrics and quaternionic toric structures in the sense of Gentili--Gori--Sarfatti. We also describe the trace foliations of the real action in the Poincaré domain. For the separate rank-one distribution $X\\Hh$, an invertible quaternionic-linear field is integrable only in the real scalar case. A nonlinear field with positive real scalar derivative at the origin and involutive $X\\Hh$ has exactly the standard quaternionic Hopf foliation on every sufficiently small centered sphere.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26269",
  "author_total": 1,
  "authors": [
    {
      "name": "Alberto Verjovsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10pcf01vxjx3h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26269",
  "fulltext_url": null,
  "id": "10pcf01vxjx3h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26269",
  "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.AT"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214068106",
  "pdf_url": "https://arxiv.org/pdf/2609.26269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10pcf01vxjx3h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2609.26269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26269"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quaternionic LVM Manifolds",
  "title_text": "Quaternionic LVM Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/10pcf01vxjx3h",
  "venue": "arXiv",
  "versions": []
}