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

• Published in: Karpats'kì matematinì publìkacìï Vol. 13; no. 2; pp. 460 - 474
• Main Authors: Ganguly, D., Dey, S., Bhattacharyya, A.
• Format: Journal Article
• Language: English
• Published: Vasyl Stefanyk Precarpathian National University 19.11.2021
• Subjects: c$-bochner curvature tensor; codazzi type ricci tensor; einstein soliton; eta$-einstein soliton; trans-sasakian manifold
• ISSN: 2075-9827; 2313-0210; 2313-0210
• DOI: 10.15330/cmp.13.2.460-474

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.