{
  "abstract": "We prove that the Fino--Vezzoni conjecture holds on every compact complex manifold carrying a Hermitian connection with parallel torsion. More precisely, if a compact connected complex manifold carries a Hermitian metric $g$ and a Hermitian connection $D$ with $DT^D=0$, then the coexistence of a balanced metric and a pluriclosed metric forces the existence of a $D$-parallel Kähler metric. The proof combines a holonomy symmetrization onto $D$-parallel forms with a finite-dimensional volume-maximization argument. In particular, the conjecture holds on every compact Bismut torsion-parallel manifold. In the non-balanced case, the obstruction of Zhao--Zheng yields the stronger conclusion that balanced and pluriclosed metrics cannot coexist.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27809",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuwen Chen"
    },
    {
      "name": "Fangyang Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4c499t1d1dcwn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27809",
  "fulltext_url": null,
  "id": "4c499t1d1dcwn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27809",
  "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"
    ]
  ],
  "openalex": "W7214176764",
  "pdf_url": "https://arxiv.org/pdf/2609.27809",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4c499t1d1dcwn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27809",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27809"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hermitian Connections with Parallel Torsion and the Fino--Vezzoni Conjecture",
  "title_text": "Hermitian Connections with Parallel Torsion and the Fino--Vezzoni Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/4c499t1d1dcwn",
  "venue": "arXiv",
  "versions": []
}