Conformally Einstein Lorentzian Lie groups: the non-solvable case
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ISSN: 0938-8974
E-ISSN: 1432-1467
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Springer-Verlag
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Abstract
We describe all left-invariant Bach-flat Lorentz metrics on non-solvable four-dimensional Lie groups, showing that they are conformally Einstein if and only if they are locally conformally flat. As a consequence we show the existence of strictly Bach-flat left-invariant metrics on SU(2)xR whose restriction to SU(2) may be positive definite, Lorentzian or degenerate.
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Calviño-Louzao, E., García-Río, E., Gutiérrez-Rodríguez, I. et al. Conformally Einstein Lorentzian Lie Groups: The Non-solvable Case. J Nonlinear Sci 35, 86 (2025). https://doi.org/10.1007/s00332-025-10183-2
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https://doi.org/10.1007/s00332-025-10183-2Sponsors
Supported by Grants ED431F 2020/04, ED431C 2023/31 (Xunta de Galicia, Spain) and PID2021-127075NA-I00, PID2022-138988NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF, EU.
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© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.