TY - JOUR AU - Ganguly, D. AU - Dey, S. AU - Bhattacharyya, A. PY - 2021/10/15 Y2 - 2024/03/28 TI - On trans-Sasakian $3$-manifolds as $\eta$-Einstein solitons: Array JF - Carpathian Mathematical Publications JA - Carpathian Math. Publ. VL - 13 IS - 2 SE - Scientific articles DO - 10.15330/cmp.13.2.460-474 UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/4275 SP - 460-474 AB - <p>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.</p> ER -