CHARACTERIZATIONS OF CONFORMAL $\eta$-EINSTEIN SOLITONS ON LP-KENMOTSU $3$-MANIFOLDS

In this manuscript, Existence of conformal $\eta$-Einstein solitons on LP-Kenmotsu manifold is discussed. We have studied conformal $\eta$-Einstein solitons on $3$-dimensional LP-Kenmotsu manifold where the Ricci tensors are Coddazi type and cyclic parallel under certain restriction of the Ricci tensor. We have also discussed second order parallel symmetric tensors admitting conformal $\eta$-Einstein solitons on $3$-dimensional LP-Kenmotsu manifolds. We also use torse-forming vector fields in addition to conformal $\eta$-Einstein solitons on $3$-dimensional LP-Kenmotsu manifolds. Finally, in $3$-dimensional LP-Kenmotsu manifold, we have a non-trivial example.