On trans-Sasakian $3$-manifolds as $\eta$-Einstein solitons

Keywords: Einstein soliton, $\eta$-Einstein soliton, trans-Sasakian manifold, Codazzi type Ricci tensor, $C$-Bochner curvature tensor
Published online: 2021-10-15


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.

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How to Cite
GangulyD.; DeyS.; BhattacharyyaA. On Trans-Sasakian $3$-Manifolds As $\eta$-Einstein Solitons. Carpathian Math. Publ. 2021, 13, 460-474.