$\eta$- Ricci Solitons on Kenmotsu manifold with Generalized Symmetric Metric Connection

TL;DR

This paper investigates $ ext{eta}$-Ricci solitons on Kenmotsu manifolds equipped with a generalized symmetric metric connection, exploring specific curvature conditions and providing an explicit example.

Contribution

It introduces the study of $ ext{eta}$-Ricci solitons on Kenmotsu manifolds with a generalized symmetric metric connection of type $(eta,eta)$, including conditions and an explicit example.

Findings

Analysis of Ricci and $ ext{eta}$-Ricci solitons under specific curvature conditions

Derivation of conditions $ar{R}.ar{S}=0$, $ar{S}.ar{R}=0$, etc.

Construction of an example of such a manifold with $ ext{eta}$-Ricci solitons

Abstract

The objective of the present paper is to study the $\eta$-Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha,\beta)$. There are discussed Ricci and $\eta$-Ricci solitons with generalized symmetric metric connection of type $(\alpha,\beta)$ satisfying the conditions $\bar{R}.\bar{S}=0$, $\bar{S}.\bar{R}=0$, $\bar{W_{2}}.\bar{S}=0$ and $\bar{S}.\bar{W_{2}}=0.$. Finally, we construct an example of Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha,\beta)$ admitting $\eta$-Ricci solitons.