η-Einstein Solitons in δ- Lorentzian Trans Sasakian Manifolds

Abstract

The object of the present research is to study the δ-Lorentzian Trans Sasakian manifolds addmitting the η-Einstein Solitons and gradient Einstein soliton. It is shown that a symmetric second order covariant tensor in a δ-Lorentzian Trans Sasakian manifold is a constant multiple of metric tensor. Also an example of η-Einstein soliton in 3-diemsional δ-Lorentzian Trans Sasakian manifold is provided in the region where δ-Lorentzian Trans Sasakian manifold expanding.