{
  "abstract": "In this paper, we show how to construct a special class of ruled hypersurfaces in the nonflat complex space forms $\\mathbb{CP}^n$ and $\\mathbb{C}H^n$. This is done by taking an arbitrary smooth curve in a totally geodesic (complex) one-dimensional submanifold and erecting an orthogonal ruling over each of its points. Concentrating on the $n=2$ case, we also examine the special situation in which the base curve has constant geodesic curvature. We show that, in this case, the construction yields precisely the real-analytic hypersurfaces of cohomogeneity one that satisfy a certain transversality condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.22979",
  "author_total": 2,
  "authors": [
    {
      "name": "Thomas A. Ivey"
    },
    {
      "name": "Patrick J. Ryan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgys3qv6fznm7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.22979",
  "fulltext_url": null,
  "id": "bgys3qv6fznm7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.22979",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7162292442",
  "pdf_url": "https://arxiv.org/pdf/2605.22979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgys3qv6fznm7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2605.22979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.22979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Cohomogeneity-One Ruled Hypersurfaces in $\\mathbb{CP}^2$ and $\\mathbb{C}H^2$",
  "title_text": "Cohomogeneity-One Ruled Hypersurfaces in ℂℙ^2 and ℂH^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/bgys3qv6fznm7",
  "venue": "arXiv",
  "versions": []
}