{
  "abstract": "In this article, we investigate rigidity results for constantly curved minimal immersions of the two-sphere $S^2$ into the unitary group $\\mathrm{U}(n)$. Using loop group methods for harmonic maps, we establish a correspondence between such immersions and a distinguished class of constantly curved holomorphic immersions of $S^2$ into finite-dimensional Grassmannians. In the case $\\mathrm{U}(3)$, we classify the constantly curved minimal immersions of $S^2$ with uniton number one and prove that, under a natural unramifiedness condition, those of uniton number two are $S^1$-invariant; as a consequence, every constantly curved totally unramified minimal immersion $S^2\\to \\mathrm{U}(3)$ of uniton number two is unitarily congruent to the composition of the first Gauss map of the Veronese curve in $\\mathbb{C}P^2$ with the Cartan embedding $\\mathbb{C}P^2\\hookrightarrow \\mathrm{U}(3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12962",
  "author_total": 2,
  "authors": [
    {
      "name": "Rui Pacheco"
    },
    {
      "name": "Mehmood Ur Rehman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15dhmx6b628ff.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12962",
  "fulltext_url": null,
  "id": "15dhmx6b628ff",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12962",
  "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": "W7212665947",
  "pdf_url": "https://arxiv.org/pdf/2609.12962",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15dhmx6b628ff.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12962",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12962"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Constantly curved minimal immersions of the two-sphere in unitary groups",
  "title_text": "Constantly curved minimal immersions of the two-sphere in unitary groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/15dhmx6b628ff",
  "venue": "arXiv",
  "versions": []
}