{
  "abstract": "We construct explicit $U(n)$-equivariant isometric embeddings $T^*\\mathbb{CP}^{n-1} \\hookrightarrow \\mathbb{R}^{n^4+2n^2-1}$, $n\\ge 2$, with respect to Calabi's hyperkähler metric on $T^*\\mathbb{CP}^{n-1}$. To achieve this, we first construct a diffeomorphism from $T^*\\mathbb{CP}^{n-1}$ onto the manifold of rank-1 projections in $M_n(\\mathbb{C})$, such that the pullback of half of the trace-class norm is a Kähler potential for the hyperkähler metric. We then use the Hilbert space structure of $M_n(\\mathbb{C})$ to produce the isometric embeddings into Euclidean space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02089",
  "author_total": 1,
  "authors": [
    {
      "name": "Joshua Lackman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/easp9sw5mct31.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02089",
  "fulltext_url": null,
  "id": "easp9sw5mct31",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02089",
  "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"
    ],
    [
      "arxiv",
      "math.SG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02089",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/easp9sw5mct31.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02089",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02089"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Isometric Embeddings of Hyperkähler $\\mathrm{T}^*\\mathbb{CP}^{n}$",
  "title_text": "Isometric Embeddings of Hyperkähler T^*ℂℙ^n",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/easp9sw5mct31",
  "venue": "arXiv",
  "versions": []
}