{
  "abstract": "Let $u:\\mathbb{S}^{2n+1}\\to\\mathbb{CP}^n$ be a smooth nonconstant harmonic map. We prove that its Morse index is equal to $ 2n+2$ if and only if \\begin{equation*} u = h \\circ π\\circ Ξ, \\end{equation*} where $Ξ:\\mathbb{S}^{2n+1}\\to\\mathbb{S}^{2n+1}$ is an isometric transformation, $π:\\mathbb{S}^{2n+1}\\to\\mathbb{CP}^n$ is the Hopf map and $h:\\mathbb{CP}^n\\to\\mathbb{CP}^n$ is a holomorphic map with degree one. When $n=1$, it refines a classical result of Urakawa and a recent result of Rivière. Moreover, we prove that $h\\circπ\\circ Ξ$ has nullity $3n^2+5n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37945",
  "author_total": 3,
  "authors": [
    {
      "name": "Qun Chen"
    },
    {
      "name": "Guofang Wang"
    },
    {
      "name": "Mingwei Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahhbk8p79qgvw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37945",
  "fulltext_url": null,
  "id": "ahhbk8p79qgvw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37945",
  "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.SP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214917148",
  "pdf_url": "https://arxiv.org/pdf/2609.37945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahhbk8p79qgvw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37945"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Harmonic maps from $\\mathbb{S}^{2n+1}$ into $\\mathbb{CP}^n$ with least Morse index",
  "title_text": "Harmonic maps from 𝕊^2n+1 into ℂℙ^n with least Morse index",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/ahhbk8p79qgvw",
  "venue": "arXiv",
  "versions": []
}