On trans-Sasakian 3-manifolds as η-Einstein solitons - Ganguly, D.; Dey, S.; Bhattacharyya, A. (Carpathian Mathematical Publications, 2021)
The present paper is to deliberate the class of 3-dimensional trans-Sasakian manifolds which admits η-Einstein solitons. We have studied η-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 η-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 η-Einstein soliton to verify our results.