{
  "abstract": "A biharmonic conformal immersion asks whether a hypersurface can become a critical point of the bienergy after a conformal change of the domain metric. We study when this flexibility can produce compact nonconstant-mean-curvature geometry in space forms. For surfaces in three-dimensional space forms, with $U=λ^2H$, Ou's system is encoded exactly by a Laplace-type operator acting on a restricted ambient Killing spinor. We classify all monic scalar--chiral factorizations of this operator. In nonzero curvature such a factorization exists locally exactly when the principal curvatures are locally constant; the normalized Euclidean branch is equally rigid, and the remaining real spherical non-CMC branch is excluded by a finite-type Frobenius obstruction. For $m>2$, this scalar rigidity does not imply geometric nonexistence. The conformal tension has independent normal and tangential components. We prove that $\\mathbb Rξ\\oplus TM$ is the minimal natural $O(m)$-equivariant carrier, derive the corresponding strongly elliptic Jacobi block and its two-grade Clifford realization, and identify off-diagonal hybridization as the escape mechanism. Exact cohomogeneity-one reductions, combined with validated interval and Chebyshev/radii-polynomial arguments, yield embedded proper non-CMC, nowhere-umbilical examples in round spheres, including $$ S^1\\times\\mathbb S^n\\times\\mathbb S^n\\hookrightarrow\\mathbb S^{2n+2} \\qquad(n\\ge1). $$ Thus the scalar obstruction is sharp with respect to coefficient bundle: the smallest enlargement forced by conformal tension already supports compact non-CMC solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20197",
  "author_total": 1,
  "authors": [
    {
      "name": "Dipesh Bhandari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1v97839chze63.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20197",
  "fulltext_url": null,
  "id": "1v97839chze63",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20197",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213581814",
  "pdf_url": "https://arxiv.org/pdf/2609.20197",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1v97839chze63.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.20197",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20197"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Biharmonic Conformal Immersions of Hypersurfaces: Dirac Rigidity and Mixed Clifford Geometry",
  "title_text": "Biharmonic Conformal Immersions of Hypersurfaces: Dirac Rigidity and Mixed Clifford Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/1v97839chze63",
  "venue": "arXiv",
  "versions": []
}