{
  "abstract": "A complete theory of null Cartan normal helices in Minkowski space-time $\\mathbb{E}^4_1$ is developed. Two algebraic conditions, obtained by successive differentiation of the helix invariant along a unit $C$-constant normal field, fully characterize null Cartan helices; the quadratic condition yields two mutually orthogonal helix axes in the Lorentzian metric. Special field types are analyzed and null Cartan cubics are shown to be normal helices. On a timelike hypersurface, a Darboux frame with six curvature functions is constructed from first principles, the normal isophotic condition is shown to reduce to a linear first-order ODE, and the existence of normal silhouettes in $\\mathbb{E}^4_1$ is established.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.01262",
  "author_total": 2,
  "authors": [
    {
      "name": "Derya Sağlam"
    },
    {
      "name": "Umut Selvi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jgy437a3e9nj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.01262",
  "fulltext_url": null,
  "id": "3jgy437a3e9nj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.01262",
  "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.GM"
    ],
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      "openalex",
      "3103|Advanced Differential Geometry Research"
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  "openalex": "W7167261297",
  "pdf_url": "https://arxiv.org/pdf/2607.01262",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jgy437a3e9nj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2607.01262",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.01262"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Null Cartan Normal Helices in Minkowski Space-Time",
  "title_text": "Null Cartan Normal Helices in Minkowski Space-Time",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/3jgy437a3e9nj",
  "venue": "arXiv",
  "versions": []
}