On trans-Sasakian $3$-manifolds as $\eta$-Einstein solitons
Copyright policy )On trans-Sasakian $3$-manifolds as $\eta$-Einstein solitons
The present paper is to deliberate the class of $3$-dimensional trans-Sasakian manifolds which admits $\eta$-Einstein solitons. We have studied $\eta$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds where the Ricci tensors are Codazzi type and cyclic parallel. We have also discussed some curvature conditions admitting $\eta$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds and the vector field is torse-forming. We have also shown an example of $3$-dimensional trans-Sasakian manifold with respect to $\eta$-Einstein soliton to verify our results.
- Jadavpur University India
Mathematics - Differential Geometry, trans-Sasakian manifold, FOS: Physical sciences, $c$-bochner curvature tensor, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Mathematical Physics (math-ph), einstein soliton, Einstein soliton, \( \eta \)-Einstein soliton, $\eta$-einstein soliton, \(C\)-Bochner curvature tensor, trans-sasakian manifold, codazzi type ricci tensor, Special Riemannian manifolds (Einstein, Sasakian, etc.), Codazzi type Ricci tensor, Differential Geometry (math.DG), 53C25, 53C15, 53C21, QA1-939, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Mathematics, Mathematical Physics
Mathematics - Differential Geometry, trans-Sasakian manifold, FOS: Physical sciences, $c$-bochner curvature tensor, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Mathematical Physics (math-ph), einstein soliton, Einstein soliton, \( \eta \)-Einstein soliton, $\eta$-einstein soliton, \(C\)-Bochner curvature tensor, trans-sasakian manifold, codazzi type ricci tensor, Special Riemannian manifolds (Einstein, Sasakian, etc.), Codazzi type Ricci tensor, Differential Geometry (math.DG), 53C25, 53C15, 53C21, QA1-939, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Mathematics, Mathematical Physics
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