{
  "abstract": "We construct an explicit dictionary between two local classifications in dimension two: normal forms of pseudo-Riemannian metrics with a quadratic integral of the geodesic flow and normal forms of $\\operatorname{gl}$-regular Nijenhuis operators. The correspondence is obtained by an explicit change of coordinates constructed from the trace and determinant of the operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05103",
  "author_total": 1,
  "authors": [
    {
      "name": "Dinmukhammed Akpan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79xhda1qc01vb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05103",
  "fulltext_url": null,
  "id": "79xhda1qc01vb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05103",
  "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.DS"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7211903390",
  "pdf_url": "https://arxiv.org/pdf/2609.05103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79xhda1qc01vb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "From quadratic integrals to Nijenhuis operators: two-dimensional dictionary",
  "title_text": "From quadratic integrals to Nijenhuis operators: two-dimensional dictionary",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/79xhda1qc01vb",
  "venue": "arXiv",
  "versions": []
}