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

Abstract

We 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.

Two Special Types of Curves in Lorentzian α-Sasakian 3-Manifolds

“…Particularly, if C is parameterized by the arc-length, the magnetic curve C is called a normal curve. For a contact Lorentzian manifold, if (M × R, J, G) belongs to the class W 4 [22], a trans-Sasakian structure [23] is an almost contact metric structure (φ α , ξ α , η α , g) on M, where J is an almost complex structure on M × R [1,[24][25][26], defined by…”

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