A Study of Conformal η-Einstein Solitons on Trans-Sasakian 3-Manifold

We study conformal η-Einstein solitons on the framework of trans-Sasakian manifold in dimension three. Existence of conformal η-Einstein solitons on trans-Sasakian manifold is discussed. Then we find some results on trans-Sasakian manifold which are conformal η-Einstein solitons where the Ricci tensor is cyclic parallel and Codazzi type. We also consider some curvature conditions with addition to conformal η-Einstein solitons on trans-Sasakian manifold. We also use torse-forming vector fields in addition to conformal η-Einstein solitons on trans-Sasakian manifold. Finally, an example of conformal η-Einstein solitons on trans-Sasakian manifold is constructed.