{
  "abstract": "In this paper, we study the Calabi curvature operator on K{ä}hler manifolds. First, we prove that if the Calabi curvature operator on K{ä}hler manifolds satisfies $\\frac{n\\left(n + 1\\right)}{2}$-positive (nonnegative), $\\frac{n + 1}{2}$-positive (nonnegative), and $\\left( n-1 \\right)$-positive (nonnegative), then the scalar curvature, Ricci curvature, and orthogonal Ricci curvature are positive (nonnegative), respectively. Second, we show that any compact K{ä}hler Einstein manifold satisfying the condition $$λ_1+\\dots+λ_α\\ge -αθ(n,α)\\barλ,\\; α\\le \\frac{n}{2}$$ must have nonnegative constant holomorphic sectional curvature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05106",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhi-Lin Dai"
    },
    {
      "name": "Hai-Ping Fu"
    },
    {
      "name": "Yao Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bgfa5yvp9bk0p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05106",
  "fulltext_url": null,
  "id": "bgfa5yvp9bk0p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05106",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7211872826",
  "pdf_url": "https://arxiv.org/pdf/2609.05106",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bgfa5yvp9bk0p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05106",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05106"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "K{ä}hler Einstein manifolds and the Calabi curvature operator",
  "title_text": "K{ä}hler Einstein manifolds and the Calabi curvature operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/bgfa5yvp9bk0p",
  "venue": "arXiv",
  "versions": []
}