Laplace and Dolbeault operators on Sasakian manifolds

[2608.27569] Laplace and Dolbeault operators on Sasakian manifolds Skip to main content Search Submit Donate Log in Mathematics > Differential Geometry arXiv:2608.27569 (math) [Submitted on 27 Aug 2026] Title: Laplace and Dolbeault operators on Sasakian manifolds Authors: Georges Habib , Ken Richardson , Robert Wolak View PDF HTML (experimental) 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 $\Delta=2\Delta_{\overline\partial}$, 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 $\Delta$ on forms depending on the eigenvalues of the Lie derivative of the Reeb vector field. Subjects: Differential Geometry (math.DG) Cite as: arXiv:2608.27569 [math.DG] (or arXiv:2608.27569v1 [math.DG] for this version) https://doi.org/10.48550/arXiv.2608.27569 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Georges Habib [ view email ] [v1] Thu, 27 Aug 2026 18:00:17 UTC (50 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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