$\eta$-RICCI SOLITONS AND GRADIENT RICCI SOLITONS ON $\delta$- LORENTZIAN TRANS-SASAKIAN MANIFOLDS

The objective of the present research article is to study the $\delta$ - Lorentzian trans- Sasakian manifolds conceding the $\eta$ - Ricci solitons and gradient Ricci soliton . We shown that a symmetric second order covariant tensor in a $\delta$ - Lorentzian trans- Sasakian manifold is a constant multiple of metric tensor. Also, we furnish an example of $\eta$ - Ricci soliton on 3- diemsional $\delta$ - Lorentzian trans- Sasakian manifold is provide in the region where $\delta$ - Lorentzian trans- Sasakian manifold is expanding. Furthermore, we discuss some results based on gradient Ricci solitons on $3$ -dimensional $\delta$ - Lorentzian trans- Sasakian manifold.