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 M3ϵ whose metrics are conformal η-Ricci-Yamabe solitons (in short, CERYS), and it is proven that if an M3ϵ with a constant scalar curvature admits a CERYS, then £Uζ is orthogonal to ζ if and only if Λ−ϵσ=−2ϵl+mr/2+1/2p+2/3. Further, we study gradient CERYS in M3ϵ and proved that an M3ϵ 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 M3ϵ has been drawn by a concrete example.