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

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.