$\eta$-Ricci solitons in $(\varepsilon)$-almost paracontact metric manifolds

TL;DR

This paper explores $\eta$-Ricci solitons within $(\varepsilon)$-almost paracontact metric manifolds, analyzing specific cases of potential vector fields and their relation to Einstein-like and $(\varepsilon)$-para Sasakian structures.

Contribution

It introduces new insights into $\eta$-Ricci solitons on these manifolds, especially when potential vector fields are characteristic or torse-forming, and examines their properties in special geometric contexts.

Findings

Characterization of $\eta$-Ricci solitons with characteristic vector fields.

Conditions for Einstein-like and $(\varepsilon)$-para Sasakian manifolds admitting $\eta$-Ricci solitons.

Results on $\eta$-Ricci solitons with parallel symmetric (0,2)-tensor fields.

Abstract

The object of this paper is to study $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds. We investigate $\eta$-Ricci solitons in the case when its potential vector field is exactly the characteristic vector field $\xi$ of the $(\varepsilon)$-almost paracontact metric manifold and when the potential vector field is torse-forming. We also study Einstein-like and $(\varepsilon)$-para Sasakian manifolds admitting $\eta$-Ricci solitons. Finally we obtain some results for $\eta$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds with a special view towards parallel symmetric (0,2)-tensor fields.