{
  "abstract": "The generalization of the Kähler metric in the complex Finsler setting admits four natural versions. Among these, the strongly Kähler--Finsler condition is known to coincide with one of the intermediate conditions. In this paper, we establish the equivalence between the weakly Kähler--Finsler condition and the remaining intermediate condition. Moreover, we obtain new necessary and sufficient conditions for a weakly Kähler--Finsler metric to be strongly Kähler--Finsler. Using these criteria, we construct, for the first time, smooth examples of weakly Kähler--Finsler metrics which are not Kähler--Finsler, via the Kobayashi metrics on smooth bounded strongly convex domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03535",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaoshu Ge"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ahs3ghcamr1m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03535",
  "fulltext_url": null,
  "id": "2ahs3ghcamr1m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03535",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7220428758",
  "pdf_url": "https://arxiv.org/pdf/2610.03535",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ahs3ghcamr1m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03535",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03535"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the Definition and Smooth Examples of Weakly Kähler--Finsler Metrics",
  "title_text": "On the Definition and Smooth Examples of Weakly Kähler--Finsler Metrics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/2ahs3ghcamr1m",
  "venue": "arXiv",
  "versions": []
}