{
  "abstract": "The Hurwitz--Radon number originates in the composition problem of quadratic forms and is related to the maximum number of pointwise linearly independent vector fields on spheres. Kannaka--Tojo [arXiv:2602.04544] reformulated the Hurwitz--Radon number in the setting of a real reductive Lie algebra $\\mathfrak g$ and its faithful representation $ι$, and introduced two natural numbers $ρ^{(1)}(\\mathfrak g,ι)$ and $ρ^{(2)}(\\mathfrak g,ι)$. For classical Lie algebras and their standard representations, these two numbers coincide except for a few cases. In this paper, fixing a Lie group $G$ and a subspace $\\mathfrak{s} $ of $ \\mathfrak g = \\operatorname{Lie}(G)$ , we define natural numbers $ρ_{G,\\mathfrak{s}}(M,σ)$ and $ρ^{\\pm}_{G,\\mathfrak{s}}(M,σ,\\nabla)$ for a $G$-manifold $(M,σ)$ equipped with an affine connection $\\nabla$. These are defined in terms of fundamental vector fields on $M$. In a special case, we show that $ρ_{G,\\mathfrak{s}}(M,σ)$ coincides with $ρ^{(2)}(\\mathfrak g,ι)$, and that $ρ^{-}_{G,\\mathfrak{s}}(M,σ,\\nabla)$ coincides with $ρ^{(1)}(\\mathfrak g,ι)$. Furthermore, we show that $ρ^{+}_{G,\\mathfrak{s}}(M,σ,\\nabla)$ is related to Clifford structures on $M$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00704",
  "author_total": 1,
  "authors": [
    {
      "name": "Muneto Miyaji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78m7yq5f7k3ba.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00704",
  "fulltext_url": null,
  "id": "78m7yq5f7k3ba",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00704",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7160181000",
  "pdf_url": "https://arxiv.org/pdf/2605.00704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78m7yq5f7k3ba.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2605.00704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00704"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Geometric Interpretation of Generalized Hurwitz--Radon Numbers Defined by Kannaka--Tojo",
  "title_text": "A Geometric Interpretation of Generalized Hurwitz--Radon Numbers Defined by Kannaka--Tojo",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/78m7yq5f7k3ba",
  "venue": "arXiv",
  "versions": []
}