{
  "abstract": "In this paper, we study some geometric properties of the disk bundles over the complete Kähler manifolds. When the base space is the complete Kähler-Einstein manifold, we compute the holomorphic sectional curvature, Riemannian sectional curvature of the complete Kähler-Einstein metric on the disk bundle. Moreover, we present a parametric criteria for whether the manifold admits negative pinched property. When the base space is a bounded pseudoconvex domain equipped with its complete Kähler metric, the corresponding ball bundle in the $k$-direct sum of line bundles is a bounded pseudoconvex Hartogs domain with fiber dimension $k$ . If the base domain is simply-connected and $k\\geq2$, we prove that the Bergman metric on such a Hartogs domain is Kähler-Einstein if and only if the domain is biholomorphically equivalent to a unit ball.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14482",
  "author_total": 4,
  "authors": [
    {
      "name": "Yihong Hao"
    },
    {
      "name": "Mingming Chen"
    },
    {
      "name": "An Wang"
    },
    {
      "name": "Ben Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f3d7tgqwqr9v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14482",
  "fulltext_url": null,
  "id": "8f3d7tgqwqr9v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14482",
  "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.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7213363482",
  "pdf_url": "https://arxiv.org/pdf/2609.14482",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8f3d7tgqwqr9v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.14482",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14482"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The curvature estimation of the complete Kähler-Einstein metrics on the disk bundles",
  "title_text": "The curvature estimation of the complete Kähler-Einstein metrics on the disk bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8f3d7tgqwqr9v",
  "venue": "arXiv",
  "versions": []
}