On the Almost $\eta-$Ricci Solitons on Pseudosymmetric Lorentz Generalized Sasakian Space Forms

Abstract

In this paper, we consider Lorentz generalized Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of \ Lorentz generalized Sasakian space forms admitting $\eta-$Ricci soliton have introduced according to the choice of some special curvature tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ Then, again according to the choice of the curvature tensor, necessary conditions are given for Lorentz generalized Sasakian space form admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made.

Keywords

• ricci-pseudosymmetric manifold
• η-ricci soliton
• generalized lorentz sasakian space form