{
  "abstract": "In this note, we prove that for n > 2 a harmonic map $\\mathbb{S}^n \\to \\mathbb{CP}^m$, of index n+1 is pseudo horizontally weakly conformal, that $n$ must be odd. In particular, for even n every non-constant harmonic map $\\mathbb{S}^n \\to \\mathbb{CP}^m$ has index at least n+2. We also present a harmonic map from $\\mathbb{S}^4$ to $\\mathrm{Gr}_{\\mathbb{C}}(2,4)$ of index 5 that is not pseudo horizontally weakly conformal, so the statement does not extend to Grassmannians.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35589",
  "author_total": 1,
  "authors": [
    {
      "name": "Surkov Egor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ah5jqayb4y44.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35589",
  "fulltext_url": null,
  "id": "1ah5jqayb4y44",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35589",
  "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": "W7214747417",
  "pdf_url": "https://arxiv.org/pdf/2609.35589",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ah5jqayb4y44.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35589",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35589"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Harmonic maps from spheres with lowest possible index and their properties",
  "title_text": "Harmonic maps from spheres with lowest possible index and their properties",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1ah5jqayb4y44",
  "venue": "arXiv",
  "versions": []
}