{
  "abstract": "In this paper, we prove that every connected closed Riemannian manifold of dimension $n\\geq4$ with $\\frac{10}{3}$-positive curvature operator of the second kind is diffeomorphic to a spherical space form. We also obtain a classification of connected closed Riemannian manifolds with $\\frac{10}{3}$-nonnegative curvature operator of the second kind. The key step is to show that $\\frac{10}{3}$-positivity implies the PIC1 condition. Finally, we give an example showing that $\\frac{10}{3}$ is optimal for deducing PIC1 from $α$-positivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26269",
  "author_total": 2,
  "authors": [
    {
      "name": "Haiqing Cheng"
    },
    {
      "name": "Kui Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/771pzq5jkqmcs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26269",
  "fulltext_url": null,
  "id": "771pzq5jkqmcs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26269",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223004070",
  "pdf_url": "https://arxiv.org/pdf/2610.26269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/771pzq5jkqmcs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26269"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sphere Theorems for $\\frac{10}{3}$-Positive Curvature Operator of the Second Kind",
  "title_text": "Sphere Theorems for 10/3-Positive Curvature Operator of the Second Kind",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/771pzq5jkqmcs",
  "venue": "arXiv",
  "versions": []
}