$\ast$-Ricci solitons and $\ast$-gradient Ricci solitons on 3-dimensional trans-Sasakian manifolds
Commun. Korean Math. Soc. 2020 Vol. 35, No. 2, 625-637
Published online April 6, 2020
Dibakar Dey, Pradip Majhi
Kolkata - 700019; Kolkata - 700019
Abstract : The object of the present paper is to characterize $3$-dimen\-sional trans-Sasakian manifolds of type $(\alpha,\beta)$ admitting $\ast$-Ricci solitons and $\ast$-gradient Ricci solitons. Under certain restrictions on the smooth functions $\alpha$ and $\beta$, we have proved that a trans-Sasakian $3$-manifold of type $(\alpha,\beta)$ admitting a $\ast$-Ricci soliton reduces to a $\beta$-Kenmotsu manifold and admitting a $\ast$-gradient Ricci soliton is either flat or $\ast$-Einstein or it becomes a $\beta$-Kenmotsu manifold. Also an illustrative example is presented to verify our results.
Keywords : Trans-Sasakian manifolds, $\ast$-Ricci soliton, $\ast$-gradient Ricci soliton, $\ast$-Einstein manifold
MSC numbers : Primary 53D15, 53C25
Supported by : The author Dibakar Dey is thankful to the Council of Scienti c
and Industrial Research, India (File no: 09/028(1010)/2017-EMR-1) for their
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