Homogeneous and curvature homogeneous Lorentzian critical metrics

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2022_rsepsa-maths_brozos_homogeneous.pdf (537.72 KB)
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URI: http://hdl.handle.net/10347/29282
ISSN: 0308-2105
E-ISSN: 1473-7124
DOI: 10.1017/prm.2022.44

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2022

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Cambridge University Press
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We determine all three-dimensional homogeneous and 1 -curvature homogeneous Lorentzian metrics which are critical for a quadratic curvature functional. As a result, we show that any quadratic curvature functional admits different non-Einstein homogeneous critical metrics and that there exist homogeneous metrics which are critical for all quadratic curvature functionals without being Einstein

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Quadratic curvature functional| Lorentzian| Critical metric| Curvature homogeneus| Homogeneus| Ricci soliton

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Brozos-Vázquez, M., Caeiro-Oliveira, S., & García-Río, E. (2022). Homogeneous and curvature homogeneous Lorentzian critical metrics. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1-25. doi:10.1017/prm.2022.44

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Supported by projects PID2019-105138GB-C21(AEI/FEDER, Spain) and ED431C 2019/10, ED431F 2020/04 (Xunta de Galicia, Spain)

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© The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited
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