A Study of Hyperbolic Yamabe Solitons on Nonreductive Four‐Dimensional Homogeneous Manifolds

The study of geometric structures on homogeneous pseudo‐Riemannian spaces ( G / H , g ) has long been an important area of research in differential geometry. Such spaces are characterized by the transitive action of a Lie group G , with the metric g being G ‐invariant using mathematical operators. However, the work of Fels and Renner shows that four‐dimensional homogeneous pseudo‐Riemannian manifolds also include nonreductive cases, where the usual reductive decomposition does not hold. These nonreductive spaces provide a rich framework for investigating various geometric structures and nonlinear systems. In this paper, we study hyperbolic Yamabe soliton vector fields, a concept introduced only recently.