Riemannian manifolds in three dimensions and ∗- η-Ricci-Yamabe solitons

In the domain of Riemannian Geometry, we explore *-rj-Ricci-Yamabe soliton on a Riemannian manifold (G3, g). Initially, we establish that if the metric g of G3 constitutes a *-rj-RicciYamabe soliton, then G3 is necessarily Einstein, when the soliton vector field V is contact. Additionally, we investigated that the Riemannian manifold (G3, g), accommodates a gradient almost *-rj-Ricci-Yamabe soliton, concluding that it must be Einstein with a consistent scalar curvature r =-6. The associated functions of the *-rj-Ricci soliton are characterized by alpha = 1 and beta= 0.