Certain properties of η-Ricci soliton on η-Einstein para-Kenmotsu manifolds

Abstract

The objective of present research paper is to be investigate the geometric properties of ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds. In this manner, we consider ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds satistfying R.S = 0. Further, we obtain results for ?-Ricci solitons on ?-Einstein para-Kenmotsu manifolds with quasi-conformal flat property. Moreover, we get result for ?-Ricci solitins in ?-Einstein para-Kenmotsu manifolds admitting Codazzi type of Ricci tensor and cyclic parallel Ricci tensor, ?-quasi-conformally semi-symmetric, ?-Ricci symmetric and quasi-conformally Ricci semi-symmetric. At last, we construct an example of a such manifold which justify the existence of proper ?-Ricci solitons