{
  "abstract": "We prove Tachibana-type rigidity theorems for closed manifolds under weakened partial-sum conditions on the eigenvalues of curvature operators. Specifically, an Einstein manifold of dimension $n\\geq4$ is locally symmetric if its curvature operator is $\\frac{2(n-1)}{3}$-nonnegative. The corresponding thresholds are $\\frac{2(n+1)}{3}$ for the primitive curvature operator of a Kähler-Einstein manifold of complex dimension $n\\geq2$, and $\\frac{2(n+2)}{3}$ for the curvature operator of a quaternionic-Kähler manifold of real dimension $4n\\geq8$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36226",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaolong Li"
    },
    {
      "name": "Peter Petersen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jn2z0pjrdejv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36226",
  "fulltext_url": null,
  "id": "5jn2z0pjrdejv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36226",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7214949569",
  "pdf_url": "https://arxiv.org/pdf/2609.36226",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jn2z0pjrdejv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36226",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36226"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Tachibana's Theorem Revisited",
  "title_text": "Tachibana's Theorem Revisited",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/5jn2z0pjrdejv",
  "venue": "arXiv",
  "versions": []
}