{
  "abstract": "We study a genus-three hyperelliptic holomorphic null-curve family in $\\mathbb{C}^4$, modelled on the algebraic data of the classical Schwarz P/D family, whose real parts define minimal immersions into $\\mathbb{R}^4$. For the order-four automorphism $ω\\mapsto iω$ of the underlying Schwarz curve, we compute explicitly its action on the four holomorphic Weierstrass $1$-forms and derive the resulting identities for all real period vectors. Consequently, for every lattice invariant under the induced target rotation, torus-period closure can be checked on one representative from each orbit of a symmetry-stable homology generating set. We also identify precisely when the additional parameter produces a nondegenerate codimension-two deformation. The paper does not claim the construction of a new embedded periodic minimal surface in $\\mathbb{R}^4$; rather, it provides an explicit symmetry reduction of the period problem associated with this family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05509",
  "author_total": 2,
  "authors": [
    {
      "name": "Erhan Güler"
    },
    {
      "name": "Magdalena Toda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqbs3p0tcr7h3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05509",
  "fulltext_url": null,
  "id": "cqbs3p0tcr7h3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05509",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212086281",
  "pdf_url": "https://arxiv.org/pdf/2609.05509",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqbs3p0tcr7h3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05509",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05509"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Schwarz-Type Null Curves in $\\mathbb{C}^4$: Symmetry and Period Reduction",
  "title_text": "Schwarz-Type Null Curves in ℂ^4: Symmetry and Period Reduction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/cqbs3p0tcr7h3",
  "venue": "arXiv",
  "versions": []
}