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

Abstract

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

20 pages

References in corpus (1)

• Ricci Solitons and Einstein-Scalar Field Theory

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• Almost $\eta$-Ricci solitons in $(LCS{)}_n$-manifolds
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