{
  "abstract": "We prove that on a compact locally conformally Kähler manifold, the existence of a non-trivial parallel vector field with respect to a Gauduchon connection $\\nabla^t$, for $t\\ne \\frac{1}{3}$, forces the metric to be either Vaisman (for $t=-1$), globally conformally Kähler (for $t=1$), or Kähler for all other values of $t$. As a consequence, we characterize compact Vaisman manifolds in terms of their Bismut holonomy group. Moreover, we show that in complex dimension two, the existence of a non-trivial $\\nabla^\\frac{1}{3}$-parallel vector field forces the metric to be globally conformally Kähler.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13657",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrei Moroianu"
    },
    {
      "name": "Giacomo Perri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cyzzkj6413qk6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13657",
  "fulltext_url": null,
  "id": "cyzzkj6413qk6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13657",
  "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": "W7221532082",
  "pdf_url": "https://arxiv.org/pdf/2610.13657",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cyzzkj6413qk6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13657",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13657"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Compact lcK manifolds with Gauduchon parallel vector fields",
  "title_text": "Compact lcK manifolds with Gauduchon parallel vector fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/cyzzkj6413qk6",
  "venue": "arXiv",
  "versions": []
}