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Peer-reviewedCC BYJournal of Geometric Analysis

New Quasi-Einstein Metrics on a Two-Sphere

  • Alex Colling1
  • Maciej Dunajski1,2
  • Hari K. Kunduri3
  • James Lucietti4
4 affiliations
  1. 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, UK
  2. 2Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland
  3. 3Department of Mathematics and Statistics and Department of Physics and Astronomy, McMaster University, Hamilton, L8S 4M1, Ontario, Canada
  4. 4School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, King’s Buildings, EH9 3FD, Edinburgh, UK
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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 m = 2 , as well as a family of new regular metrics with m≠ 2 m ≠ 2 given in terms of hypergeometric functions. We also show that in the case m=−1 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.

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Cite

BibTeXRIS
BibTeX
@article{colling2026quasieinstein,
  title = {{New Quasi-Einstein Metrics on a Two-Sphere}},
  author = {Alex Colling and Maciej Dunajski and Hari K. Kunduri and James Lucietti},
  journal = {Journal of Geometric Analysis},
  year = {2026},
  month = may,
  doi = {10.1007/s12220-026-02459-0},
  url = {https://doi.org/10.1007/s12220-026-02459-0},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - New Quasi-Einstein Metrics on a Two-Sphere
AU  - Alex Colling
AU  - Maciej Dunajski
AU  - Hari K. Kunduri
AU  - James Lucietti
PY  - 2026
DA  - 2026/05/16
JO  - Journal of Geometric Analysis
DO  - 10.1007/s12220-026-02459-0
UR  - https://doi.org/10.1007/s12220-026-02459-0
AB  - 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 m = 2 , as well as a family of new regular metrics with m≠ 2 m ≠ 2 given in terms of hypergeometric functions. We also show that in the case m=−1 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.
SN  - 1050-6926
SN  - 1559-002X
ER  -