Normal Paracontact Metric Space Forms Admitting Almost $\eta-$Ricci Solitons

Abstract

In this paper, we have considered normal paracontact metric space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of normal paracontact metric space forms admitting $\eta-$Ricci soliton have introduced according to the choosing of some special curvature tensors such as Riemann, concircular, projective and $W_{1}$ curvature tensor$.$ After then, according to the choice of the curvature tensors, necessary conditions are given for normal paracontact metric space form admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made under the some conditions.

Keywords

• Ricci-pseudosymmetric Manifold
• η-Ricci Soliton
• Normal Paracontact Metric Space Form

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