{
  "abstract": "Sprays of scalar curvature constitute an important class of sprays, and such a class includes all two-dimensional sprays. In this paper, we consider the global metrizability of certain sprays on a manifold under some curvature and topological conditions. We prove that, for a regular spray {\\bf G} of scalar curvature with almost everywhere nonzero Ricci curvature on a manifold $M$ of dimension $n\\ge 3$, {\\bf G} is globally metrizable if and only if it is locally metrizable, provided that $M$ has trivial first de Rham cohomology group. Further, we characterize the global metizability of a class of two-dimensional singular Berwald sprays on a manifold with trivial first de Rham cohomology group. Meanwhile, on a cylinder $S^1\\times {\\bf R}$ (with non-trivial first de Rham cohomology group), we construct a family of singular Berwald sprays which are locally metrizable but not globally metrizable. Finally, we construct some examples of two-dimensional sprays on cylinders or spheres with special properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18292",
  "author_total": 2,
  "authors": [
    {
      "name": "Xingzhi Duanmu"
    },
    {
      "name": "Guojun Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wywbxpekrznx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18292",
  "fulltext_url": null,
  "id": "2wywbxpekrznx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18292",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7213510565",
  "pdf_url": "https://arxiv.org/pdf/2609.18292",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wywbxpekrznx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18292",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18292"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Global Metrizability on Sprays of Scalar Curvature",
  "title_text": "Global Metrizability on Sprays of Scalar Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/2wywbxpekrznx",
  "venue": "arXiv",
  "versions": []
}