$\left(LCS\right)_{n}-$Manifolds Admitting Almost $\eta-$Ricci Solitons on Some Special Curvature Tensors

Abstract

In this paper, we consider $\left(LCS\right)_{n}$ manifold admitting almost $\eta-$Ricci solitons by means of curvature tensors. Ricci pseudosymmetry concepts of $\left(LCS\right)_{n}$ manifold admitting $\eta-$Ricci soliton have introduced according to the choice of some special curvature tensors such as pseudo-projective, $W_{1}$, $W_{1}^{\ast}$ and $W_{2}.$ Then, again according to the choice of the curvature tensor, necessary conditions are searched for $\left(LCS\right)_{n}$ manifold admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made.