Riemann Solitons on a Spacetime with the Spatially Homogeneous Rotating Metric

This manuscript presents a comprehensive taxonomy of Riemann solitons within the framework of a spacetime manifold endowed with a metric exhibiting both spatial homogeneity and rotational characteristics. Furthermore, we undertake an analysis to determine the geometric nature of these solitons by establishing their correspondence to Killing vector fields, Ricci collineation vector fields, and gradient vector fields.