[2403.04117] New quasi-Einstein metrics on a two-sphere Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2403.04117 (math) [Submitted on 7 Mar 2024 ( v1 ), last revised 24 Apr 2026 (this version, v3)] Title: New quasi-Einstein metrics on a two-sphere Authors: Alex Colling , Maciej Dunajski , Hari Kunduri , James Lucietti View a PDF of the paper titled New quasi-Einstein metrics on a two-sphere, by Alex Colling and 3 other authors View PDF HTML (experimental) Abstract: We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics with $m\neq 2$ given in terms of hypergeometric functions. We also show that in the case $m=-1$ with vanishing cosmological constant the only orientable compact solution in dimension two is the flat torus, which proves that there are no compact surfaces with a metrisable affine connection with skew Ricci tensor. Comments: v2: minor edits, reference added. v3: minor edits, to appear in the Journal of Geometric Analysis Subjects: Differential Geometry (math.DG) ; General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th) Cite as: arXiv:2403.04117 [math.DG] (or arXiv:2403.04117v3 [math.DG] for this version) https://doi.org/10.48550/arXiv.2403.04117 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Geom. Anal. 36, 226 (2026) Related DOI : https://doi.org/10.1007/s12220-026-02459-0 Focus to learn more DOI(s) linking to related resources Submission history From: James Lucietti [ view email ] [v1] Thu, 7 Mar 2024 00:12:16 UTC (68 KB) [v2] Mon, 18 Mar 2024 13:28:19 UTC (67 KB) [v3] Fri, 24 Apr 2026 13:17:07 UTC (69 KB) Full-text links: Access Paper: View a PDF of the paper titled New quasi-Einstein metrics on a two-sphere, by Alex Colling and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2024-03 Change to browse by: gr-qc hep-th math References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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) Major funding support from