{
  "abstract": "We give a proof of a folklore conjecture that a compact Kähler manifold with the same scalar Laplace spectrum as complex projective space equipped with the Fubini--Study metric is holomorphically isometric to it. More generally, we prove that the spectrum of the Hodge Laplacian in any one fixed degree $p$ determines $\\CP^n$ up to holomorphic isometry among compact connected Kähler manifolds, for every fixed pair of integers $(p,n)$ with $0\\leq p\\leq n$. Equality of a single Hodge spectrum first forces periodic geodesic flow and the integral cohomology ring of complex projective space. The ordinary first heat coefficient then identifies the total scalar curvature except on a Pell sequence of pairs. For those pairs, a clean wave-trace argument, a Krawtchouk estimate, and a mod-two projective-bundle obstruction determine the geodesic return holonomy. A canonical Kähler involution recovers a weighted first heat coefficient which is nonzero throughout the exceptional sequence. The Kobayashi--Ochiai theorem and a fixed-class second-heat-coefficient calculation complete the argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03536",
  "author_total": 2,
  "authors": [
    {
      "name": "Kefeng Liu"
    },
    {
      "name": "Hao Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9jt8pmmvt82jw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03536",
  "fulltext_url": null,
  "id": "9jt8pmmvt82jw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03536",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9jt8pmmvt82jw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A proof of the spectral rigidity for complex projective space",
  "title_text": "A proof of the spectral rigidity for complex projective space",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/9jt8pmmvt82jw",
  "venue": "arXiv",
  "versions": []
}