{
  "abstract": "We investigate the existence conditions for coupled extremal Kähler metrics on minimal ruled surfaces over a genus 2 Riemann surface. Using the Calabi ansatz to reduce the coupled extremal equations to ordinary differential equations, we prove that a pair of coupled extremal metrics exists for normalized Kähler classes $Ω_a$ and $Ω_b$ if and only if their parameters $(a, b)$ belong to an explicitly defined open region $\\mathcal{S}_{\\mathrm{ext}}$ in the positive real quadrant. Furthermore, we show that this existence region inherently contains the diagonal segment corresponding to classical extremal Kähler metrics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18418",
  "author_total": 1,
  "authors": [
    {
      "name": "Ramesh Mete"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9hn673hxzwhk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18418",
  "fulltext_url": null,
  "id": "c9hn673hxzwhk",
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  "landing_url": "https://arxiv.org/abs/2609.18418",
  "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.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
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  "openalex": "W7213503672",
  "pdf_url": "https://arxiv.org/pdf/2609.18418",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9hn673hxzwhk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18418",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18418"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the existence of coupled extremal Kähler metrics on ruled surfaces",
  "title_text": "On the existence of coupled extremal Kähler metrics on ruled surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/c9hn673hxzwhk",
  "venue": "arXiv",
  "versions": []
}