Some critical metrics over four-dimensional homogeneous pseudo-Riemannian manifolds

In this paper, we investigated the existence of non-Einstein homogeneous critical metrics on homogeneous pseudo-Riemannian four-manifolds with non-trivial isotropy. Specifically, we focused on the presence of these metrics within four-dimensional non-reductive homogeneous manifolds. Our study aims to shed light on the underlying geometric structures and contribute to a deeper understanding of these mathematical constructs.