Abstract

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.

Keywords and Phrases

Conformal $\eta$-Einstein solitons, LP-Kenmotsu manifold, codazzi type Ricci tensor, Second order parallel symmetric tensors.

A.M.S. subject classification

Primary 53C15, Secondary 53C25.

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