{
  "abstract": "We study Hamiltonian stationary Lagrangian surfaces in complex space forms with nowhere-zero mean curvature vector $H$. We prove that if the Gaussian curvature is constant and $\\grad|H|$ has positive constant length, then both the surface and the ambient space are flat. Moreover, the immersion is locally congruent to the known surface obtained as the product of a Cornu spiral and its reflection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18508",
  "author_total": 1,
  "authors": [
    {
      "name": "Toru Sasahara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/07w7yh9fn1wey.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18508",
  "fulltext_url": null,
  "id": "07w7yh9fn1wey",
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  "landing_url": "https://arxiv.org/abs/2609.18508",
  "language": null,
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  "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",
      "2604|Geometric Analysis and Curvature Flows"
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  ],
  "openalex": "W7213514630",
  "pdf_url": "https://arxiv.org/pdf/2609.18508",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/07w7yh9fn1wey.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18508",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18508"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature",
  "title_text": "Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/07w7yh9fn1wey",
  "venue": "arXiv",
  "versions": []
}