Brozos-Vázquez, MiguelCaeiro-Oliveira, SandroGarcia-Rio, Eduardo2024-07-052024-07-052022Brozos-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.2022.1263540022-247Xhttp://hdl.handle.net/2183/37743Accepted manuscript[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.eng© 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/http://creativecommons.org/licenses/by-nc-nd/3.0/es/Quadratic curvature functionalCritical metricCurvature homogeneousSemi-symmetricjournal articleopen accesshttps://doi.org/10.1016/j.jmaa.2022.126354