{
  "abstract": "Let $(M^{2m},g,f,J)$ be a complete nonsteady gradient Kähler-Ricci soliton satisfying $\\mathrm{Ric}+\\nabla^2 f=λg$, $λ\\neq 0$. We prove that constant scalar curvature forces the soliton to be rigid. More precisely, the universal cover splits holomorphically and isometrically as $N^{2k}\\times\\mathbb{C}^{m-k}$, where $N^{2k}$ is Kähler-Einstein with $\\mathrm{Ric}_{g_N}=λg_N$. In the shrinking case the quotient is trivial; in the normalization $λ=1/2$ one has $R\\equiv k$. The Kähler result rests on a Riemannian rigidity criterion. On a complete nonsteady gradient Ricci soliton, if $\\mathcal{L}_{\\nabla f}\\mathrm{Ric}$ is nonnegative or nonpositive everywhere, then it vanishes and the soliton is rigid; no assumption on the scalar curvature is needed. Along the Ricci flow generated by the soliton, this means that a Ricci tensor that is monotone in time is constant in time, and that this forces rigidity. We also give a direct proof that the pinching $0\\leq\\mathrm{Ric}\\leqλg$ forces constant scalar curvature and radial flatness, yielding the rigidity conclusion through the Petersen-Wylie characterization. The proof combines a weighted cutoff argument with a partial Codazzi symmetry for the Ricci endomorphism.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11935",
  "author_total": 5,
  "authors": [
    {
      "name": "Matheus Horácio"
    },
    {
      "name": "Wenqi Li"
    },
    {
      "name": "Jianyu Ou"
    },
    {
      "name": "Guoqiang Wu"
    },
    {
      "name": "Detang Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7k0x51w07swr0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11935",
  "fulltext_url": null,
  "id": "7k0x51w07swr0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11935",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7221142762",
  "pdf_url": "https://arxiv.org/pdf/2610.11935",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7k0x51w07swr0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11935",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11935"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Rigidity of Kähler-Ricci Solitons with Constant Scalar Curvature",
  "title_text": "Rigidity of Kähler-Ricci Solitons with Constant Scalar Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/7k0x51w07swr0",
  "venue": "arXiv",
  "versions": []
}