Open AccessOn trans-Sasakian $3$-manifolds as $\eta$-Einstein solitons
Author(s) -
Dipen Ganguly,
Santu Dey,
Arindam Bhattacharyya
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.2.460-474
Subject(s) - einstein , ricci flat manifold , manifold (fluid mechanics) , soliton , einstein manifold , mathematical physics , curvature , mathematics , pure mathematics , vector field , field (mathematics) , physics , mathematical analysis , ricci curvature , scalar curvature , geometry , quantum mechanics , nonlinear system , mechanical engineering , engineering
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.