{
  "abstract": "We establish a Bochner formula for double forms in terms of the curvature operator of the second kind. As an application, we prove that a complete Riemannian manifold of dimension $n \\ge 4$ with harmonic Weyl tensor and $\\frac{3(n-1)}{4}$-nonnegative curvature operator of the second kind is either globally conformally equivalent to a space of positive constant curvature or is isometric to a flat manifold. We prove vanishing theorems for the Lichnérowicz Laplacian $Δ$ on $(p,q)$ double forms. These generalize recent results of Nienhaus-Petersen-Wink \\cite{NPW23} and Dai-Fu-Lu-Yang \\cite{DF24,DFY24,FL1,FLD}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10325",
  "author_total": 2,
  "authors": [
    {
      "name": "Hai-Ping Fu"
    },
    {
      "name": "Yao Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ps79mshffrfe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10325",
  "fulltext_url": null,
  "id": "2ps79mshffrfe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10325",
  "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",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7220901231",
  "pdf_url": "https://arxiv.org/pdf/2610.10325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ps79mshffrfe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Some vanishing theorems on $(p,q)$ double form and curvature operator of the second kind",
  "title_text": "Some vanishing theorems on (p,q) double form and curvature operator of the second kind",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/2ps79mshffrfe",
  "venue": "arXiv",
  "versions": []
}