Curvature homogeneous critical metrics in dimension three

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. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

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