{
  "abstract": "Sasakian manifolds, the odd-dimensional analogues of Kähler manifolds, carry two natural pairs of first-order Dolbeault-type operators on the full complex of differential forms, extending the Kohn--Rossi differentials. On such Sasaki manifolds, we establish Kähler-type identities for these operators, and relate the resulting Dolbeault Laplacians to the Hodge Laplacian. Unlike the Kähler case, where $Δ=2Δ_{\\overline\\partial}$, the relation has extra terms coming from the Reeb flow. Using these formulas and a Lefschetz decomposition, we derive lower and upper eigenvalue estimates for $Δ$ on forms depending on the eigenvalues of the Lie derivative of the Reeb vector field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27569",
  "author_total": 3,
  "authors": [
    {
      "name": "Georges Habib"
    },
    {
      "name": "Ken Richardson"
    },
    {
      "name": "Robert Wolak"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzeh98rq3fcyv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27569",
  "fulltext_url": null,
  "id": "bzeh98rq3fcyv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27569",
  "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": "W7204793309",
  "pdf_url": "https://arxiv.org/pdf/2608.27569",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzeh98rq3fcyv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27569",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27569"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Laplace and Dolbeault operators on Sasakian manifolds",
  "title_text": "Laplace and Dolbeault operators on Sasakian manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/bzeh98rq3fcyv",
  "venue": "arXiv",
  "versions": []
}