{
  "abstract": "Biconservative submanifolds arise as a natural relaxation of the biharmonic condition and play an important role in the submanifold theory. In this paper, we study non-CMC biconservative surfaces with parallel normalized mean curvature vector field (PNMC surfaces) in the four-dimensional hyperbolic space $\\mathbb{H}^4$, for which we consider the hyperboloid model. We provide a local extrinsic description of such surfaces, showing that they are generated by a directrix curve lying in a totally geodesic hypersurface $\\mathbb{H}^3$ of $\\mathbb{H}^4$, through a certain normal flow. This extrinsic classification of non-CMC, PNMC biconservative surfaces in $\\mathbb{H}^4$ splits naturally into three cases according to the type of a certain vector field, which can be non-zero null, spacelike or timelike. We also prove that these surfaces are invariant under the action of a parabolic, elliptic, and hyperbolic one-parameter group of isometries of $\\mathbb{H}^4$, respectively. Moreover, their full groups of ambient isometries preserving the surfaces are determined. Together with the previous results, the classification of non-CMC, PNMC surfaces in four-dimensional space forms is now complete, from both intrinsic and extrinsic points of view.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.22396",
  "author_total": 2,
  "authors": [
    {
      "name": "Simona Nistor"
    },
    {
      "name": "Mihaela Rusu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5v9rky0jycjr6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.22396",
  "fulltext_url": null,
  "id": "5v9rky0jycjr6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.22396",
  "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": "W7162114512",
  "pdf_url": "https://arxiv.org/pdf/2605.22396",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5v9rky0jycjr6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2605.22396",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.22396"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Extrinsic characterizations of biconservative surfaces in the $4$-dimensional hyperbolic space",
  "title_text": "Extrinsic characterizations of biconservative surfaces in the $4$-dimensional hyperbolic space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5v9rky0jycjr6",
  "venue": "arXiv",
  "versions": []
}