2022 # 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 additio…

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“…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…”

confidence: 99%

“…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…”

confidence: 99%

“…For (α, β) trans-Sasakian structures, if β = 0, that manifold will become an α-Sasakian manifolds. Sasakian manifolds appear as examples of α-Sasakian manifolds with α = 1 and β = 0 in [1]. In 2005, Yildiz and Murathan introduced the notions of Lorentzian α-Sasakian manifolds [2].…”

confidence: 99%

“…Recently, Wang [50] proved that if the metric of a Kenmotsu 3-manifold represents a * -Ricci soliton, then the manifold is locally isometric to the hyperbolic space H 3 (−1). Moreover, we can get more latest studies equipped with soliton geometry in [12,18,31,39,40,55].…”

confidence: 99%