Notes on ?-Einstein solitons on para-Kenmotsu manifolds

The present paper deals with the investigation of Para-Kenmotsu manifolds admitting ?-Einstein solitons. Some necessary conditions for such manifolds to be Einstein are given, and it is proven that if a para-Kenmotsu manifold E admits an ?-Einstein soliton, then the manifold E is Einstein. Then, some noteworthy characterizations that classify para-Kenmotsu manifolds admitting such solitons are obtained.

Automated summary

This paper investigates the existence of ?-Einstein solitons in Para-Kenmotsu manifolds. Necessary conditions for such manifolds to be Einstein are given, and it is proven that if a para-Kenmotsu manifold E admits an ?-Einstein soliton, then E is an Einstein manifold. Furthermore, noteworthy characterizations that classify para-Kenmotsu manifolds admitting such solitons are obtained.