∗-RICCI SOLITONS AND ∗-GRADIENT RICCI SOLITONS ON 3-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS
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초록
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.
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.
참고문헌 (22)
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