{
  "abstract": "In this paper, we study hypersurfaces $M^4$ in the Minkowski space $\\mathbb{E}^5_1$ whose shape operator $S$ is non-diagonalizable, having a triple real eigenvalue $λ$ with a one-dimensional eigenspace together with a simple eigenvalue $μ$ (Case~(iii) in the classification of Magid). Assuming that $λ$ and $μ$ satisfy a functional relation $λ=f(μ)$ and that the eigenvector field of $μ$ is geodesic, we show that $λ$ and $μ$, as well as the pseudo-orthonormal frame, are intrinsic invariants of $M$, determined by the induced metric up to sign. As a consequence, we prove that such hypersurfaces are unique up to isometries of $\\mathbb{E}^5_1$. We also obtain a classification of the warped product hypersurfaces of this type.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18896",
  "author_total": 2,
  "authors": [
    {
      "name": "Zülal Derin Yaqub"
    },
    {
      "name": "Nurettin Cenk Turgay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fk4bqntf809n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18896",
  "fulltext_url": null,
  "id": "2fk4bqntf809n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18896",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7222060662",
  "pdf_url": "https://arxiv.org/pdf/2610.18896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fk4bqntf809n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.18896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hypersurfaces with Non-diagonalizable Shape Operators in Minkowski Spaces",
  "title_text": "Hypersurfaces with Non-diagonalizable Shape Operators in Minkowski Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/2fk4bqntf809n",
  "venue": "arXiv",
  "versions": []
}