{
  "abstract": "Let $M$ be either $\\mathbb{CP}^n$ or $\\mathbb{HP}^n$. We prove that the family $\\overline{\\mathcal{F}}=\\{Σ_σ\\}_{σ\\in M}$ of minimal geodesic spheres in $M$ characterizes the Fubini-Study metric $\\overline{g}$, that is, $\\overline{g}$ is the only metric that makes these real hypersurfaces minimal. This result is related to the recent theory of Zoll families of minimal hypersurfaces $(M,g,\\mathcal{F}=\\{Σ_σ\\})\\in\\mathcal{Z}$. It is conjectured that the only Zoll metric in $\\mathbb{CP}^n$ is $\\overline{g}$. We present evidence that suggests a similar rigidity of $(\\mathbb{CP}^n,\\overline{g},\\overline{\\mathcal{F}})$ in this context of minimal hypersurfaces. Namely, we show that a direct adaptation of Guillemin's Theorem for conformal deformations of Zoll metrics in $\\mathbb{S}^2$ is not possible for $(\\mathbb{CP}^n,\\overline{g},\\overline{\\mathcal{F}})$, when $p=2n-1$ is a prime number.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25379",
  "author_total": 1,
  "authors": [
    {
      "name": "Diego Guajardo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/848rhv71twg49.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25379",
  "fulltext_url": null,
  "id": "848rhv71twg49",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25379",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223011655",
  "pdf_url": "https://arxiv.org/pdf/2610.25379",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/848rhv71twg49.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25379",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25379"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Oriented Zoll families of minimal hypersurfaces in $\\mathbb{CP}^n$ and $\\mathbb{HP}^n$",
  "title_text": "Oriented Zoll families of minimal hypersurfaces in ℂℙ^n and ℍℙ^n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/848rhv71twg49",
  "venue": "arXiv",
  "versions": []
}