$\ast$-Ricci solitons and $\ast$-gradient Ricci solitons on 3-dimensional trans-Sasakian manifolds
Commun. Korean Math. Soc.
Published online January 28, 2020
Dibakar Dey and Pradip Majhi
University of Calcutta, Assistant Professor
Abstract : The object of the present paper is to characterize $3$-dimensional trans-Sasakian manifolds of type $(\alpha,\beta)$ admitting $\ast$-Ricci soliton and $\ast$-gradient Ricci soliton. Under certain restrictions on the smooth function $\alpha$ and $\beta$, we have proved that a $(\alpha,\beta)$-trans-Sasakian $3$-manifold admitting $\ast$-Ricci soliton reduces to a $\beta$-Kenmotsu manifold and admitting $\ast$-gradient Ricci soliton is either flat or $\ast$-Einstein or 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 : 53D15, 53C25
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