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

Year 2023, Volume: 6 Issue: 2, 43 - 52, 01.07.2023

Tuğba Mert , Mehmet Atçeken

https://doi.org/10.32323/ujma.1236596

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

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