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

Key Points

• The aim is to explore non-Einstein homogeneous critical metrics in pseudo-Riemannian four-manifolds with non-trivial isotropy.
• Investigated the existence of non-Einstein homogeneous critical metrics
• Focused on four-dimensional non-reductive homogeneous manifolds
• Analyzed geometric structures associated with these metrics.
• Identified conditions under which non-Einstein metrics exist
• Presented insights into the geometric structures of four-dimensional manifolds
• Contributed to the understanding of homogeneous pseudo-Riemannian spaces.