A Study of Conformal $$\eta$$-Einstein Solitons on Trans-Sasakian 3-Manifold

Abstract

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