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Curvature homogeneous critical metrics in dimension three

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URI: http://hdl.handle.net/2183/37743
DOI: https://doi.org/10.1016/j.jmaa.2022.126354

Publication date

2022

Authors

Caeiro-Oliveira, Sandro
Garcia-Rio, Eduardo

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Bibliographic citation

Brozos-Vázquez, M., Caeiro-Oliveira, S., García-Río, E., 2022. Curvature homogeneous critical metrics in dimension three. Journal of Mathematical Analysis and Applications 514, 126354. https://doi.org/10.1016/j.jmaa.2022.126354

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Abstract

[Abstract] We study curvature homogeneous three-manifolds modeled on a symmetric space which are critical for some quadratic curvature functional. If the Ricci operator is diagonalizable, critical metrics are 1-curvature homogeneous Brinkmann waves and are critical for one specific functional. Otherwise, critical metrics are modeled on Cahen-Wallach symmetric spaces and they are Kundt spacetimes which are critical for all quadratic curvature functionals.

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Accepted manuscript

Keywords

Quadratic curvature functional Critical metric Curvature homogeneous Semi-symmetric

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https://doi.org/10.1016/j.jmaa.2022.126354

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© 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

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© 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

Except where otherwise noted, this item's license is described as © 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/