$η$-Ricci Solitons on $β$-Kenmotsu Manifolds - R. L. Patel; R. N. Singh (International Journal of Mathematics And its Applications, 2021)
$η $-Ricci solitons on $β $-Kenmotsu manifold satisfying certain curvature conditions $R(ξ,X).S=0$, $S(ξ,X).R=0$, $W_{2}\left(ξ ,X\right).S=0$ and $S\left(ξ,X\right).W_{2}=0$. We proved that in $β $-Kenmotsu manifold $(M,φ,ξ,η,g)$. Then the existence of an $η $-Ricci solitons implies that M is Einstein manifold and if the Ricci curvature tensor satisfies, $S(ξ,X).R=0$, then Ricci solitons M is steady. If the condition $μ =0$, then $λ =0$, which shows that $λ $ is steady.