{
  "abstract": "In this paper, we study cylindrically symmetric projectively flat Finsler metrics \\(F=|\\bar y|ϕ(x^0,r,s,z)\\). We reformulate the conditions for projective flatness and strong convexity in terms of \\(Ω=ϕ-sϕ_s-zϕ_z\\), isolating the compatibility condition missing in earlier work. Using the method of characteristics, we give an integral formula for all smooth local solutions near points with \\(r>0\\) and \\(s=z=0\\). These solutions are determined by a characteristic potential up to the addition of an invariant exact one-form. In the reversible case, the equation for the potential reduces to a \\((2+1)\\)-dimensional wave equation on a half-space. We illustrate the reconstruction with a polynomial potential and compute the potentials of a known family of spherically symmetric metrics and their linear pullbacks. The convexity conditions also admit decreasing profiles and recover the spherical Beltrami metric as a particular case. Finally, suitable positive sums of linear pullbacks yield smooth reversible projectively flat Finsler metrics on \\(\\mathbb R^{n+1}\\) whose tangent norm at the origin is non-Riemannian. Consequently, these metrics are not linear pullbacks of spherically symmetric metrics",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08747",
  "author_total": 3,
  "authors": [
    {
      "name": "Newton Solórzano"
    },
    {
      "name": "Víctor León"
    },
    {
      "name": "Dik Lujerio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6keynt6xv4yp0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08747",
  "fulltext_url": null,
  "id": "6keynt6xv4yp0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08747",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08747",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6keynt6xv4yp0.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08747",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08747"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Projective flatness of cylindrically symmetric Finsler metrics",
  "title_text": "Projective flatness of cylindrically symmetric Finsler metrics",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/6keynt6xv4yp0",
  "venue": "arXiv",
  "versions": []
}