{
  "abstract": "The Dinew--Popovici functional is an energy functional for Hermitian symplectic metrics in a fixed Aeppli cohomology class. Its vanishing characterizes the Kähler metrics in that class, providing a variational approach to Kähler geometry. Dinew and Popovici proved that every critical point is Kähler in complex dimension three. We give a negative answer to Erfan Soheil's question about higher dimensions by constructing non-Kähler critical metrics on products of two Kähler surfaces $(S_1,η_1)$ and $(S_2,η_2)$. These metrics are critical under every variation on the product 4-fold. We characterize the critical product metrics and prove that non-Kähler critical products exist in the Aeppli class $[η_1+η_2]_A$ precisely when the canonical bundles of the two surface factors are smoothly trivial. As a by-product, we develop a geometric flow driven by the torsion tensor and converging to the fixed Kähler background when this background metric has nonnegative holomorphic bisectional curvature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08113",
  "author_total": 1,
  "authors": [
    {
      "name": "Hanwen Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dk23e80hg2n98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08113",
  "fulltext_url": null,
  "id": "dk23e80hg2n98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08113",
  "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": "W7212053614",
  "pdf_url": "https://arxiv.org/pdf/2609.08113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dk23e80hg2n98.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Non-Kähler Critical Hermitian Metrics of the Dinew--Popovici Functional",
  "title_text": "Non-Kähler Critical Hermitian Metrics of the Dinew--Popovici Functional",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/dk23e80hg2n98",
  "venue": "arXiv",
  "versions": []
}