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

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 $\bar{R}.\bar{S}=0$, $\bar{S}.\bar{R}=0$, $\overline{W_2}.\bar{S}=0$ and $\bar{S}.\overline{W_2}=0.$. Finally, we construct an example of Kenmotsu manifold with generalized symmetric metric connection of type $(\alpha ,\beta )$ admitting $\eta$-Ricci solitons.

arXiv admin note: substantial text overlap with arXiv:1804.10020; text overlap with arXiv:1402.0223 by other authors