Advanced Studies: Euro-Tbilisi Mathematical Journal

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

H. G. Nagaraja, R. C. Pavithra, M. Sangeetha

In the domain of Riemannian Geometry, we explore *-η-Ricci-Yamabe soliton on a Riemannian manifold (G³, g). Initially, we establish that if the metric g of G³ constitutes a *-η-Ricci-Yamabe 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 *-η-Ricci-Yamabe soliton, concluding that it must be Einstein with a consistent scalar curvature r=-6, The associated functions of the *-η-Ricci soliton are characterized by α=1 and β=0.


Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(3) (2024), pp. 181-193