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 M3(ϵ) whose metrics are conformal η-Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M3(ϵ) with a constant scalar curvature admits a CERYS, then £Uζ is orthogonal to ζ if and only if Λ − ϵσ = −2ϵl + (mr/2) + (1/2)(p + (2/3)). Further, we study gradient CERYS in M3(ϵ) and proved that an M3ðϵÞ 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 M3(ϵ) has been drawn by a concrete example.