Conformal η-Ricci-Yamabe Solitons within the Framework of ϵ-LP-Sasakian 3-Manifolds.

In the present note, we study ϵ -LP-Sasakian 3-manifolds M 3 ϵ whose metrics are conformal η -Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M 3 ϵ with a constant scalar curvature admits a CERYS, then £ U ζ is orthogonal to ζ if and only if Λ − ϵ σ = − 2 ϵ l + m r / 2 + 1 / 2 p + 2 / 3 . Further, we study gradient CERYS in M 3 ϵ and proved that an M 3 ϵ admitting gradient CERYS is a generalized conformal η -Einstein manifold; moreover, the gradient of the potential function is pointwise collinear with the Reeb vector field ζ. Finally, the existence of CERYS in an M 3 ϵ has been drawn by a concrete example. [ABSTRACT FROM AUTHOR]