Homogeneous and curvature homogeneous Lorentzian critical metrics

Brozos-Vázquez, Miguel; Caeiro-Oliveira, Sandro; Garcia-Rio, Eduardo

Use this link to cite:

http://hdl.handle.net/2183/37717

Homogeneous and curvature homogeneous Lorentzian critical metrics

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Brozos-Vazquez_M_2023_Homogeneous_and_curvature_homogeneous_lorentzian_critical_metrics.pdf (610.27 KB)

Identifiers

URI: http://hdl.handle.net/2183/37717

DOI: https://doi.org/10.1017/prm.2022.44

Publication date

2023

Authors

Brozos-Vázquez, Miguel

Caeiro-Oliveira, Sandro

Garcia-Rio, Eduardo

Bibliographic citation

Brozos-Vázquez M, Caeiro-Oliveira S, García-Río E. Homogeneous and curvature homogeneous Lorentzian critical metrics. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2023;153(4):1272-1296. doi:10.1017/prm.2022.44

Abstract

[Abstract] 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.