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.
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2011 ◽
Vol 57
(2)
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pp. 417-440
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2018 ◽
Vol 33
(2)
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pp. 217
2019 ◽
Vol 16
(03)
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pp. 1950039
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2021 ◽
pp. 2150169
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