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The objective of the present research article is to study the δ-Lorentzian trans-Sasakian manifolds concidering the η-Ricci solitons and gradient Ricci soliton. We have shown that a symmetric second order covariant tensor in a δ-Lorentzian trans-Sasakian manifold is a constant multiple of metric tensor. Also, we have provided an example of η-Ricci soliton on 3-diemsional δ-Lorentzian trans-Sasakian manifold in the region where δ-Lorentzian trans-Sasakian manifold is expanding. Furthermore, we have discussed the results based on gradient Ricci solitons on 3-dimensional δ-Lorentzian trans-Sasakian manifold. [ABSTRACT FROM AUTHOR]

In this work, we have investigated a new deformation of almost contact metric manifolds. New relations between classes of 3-dimensional almost contact metric have been discovered. Several concrete examples are discussed. [ABSTRACT FROM AUTHOR]