*-RICCI SOLITONS AND *-GRADIENT RICCI SOLITONS ON 3-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS

摘要

The object of the present paper is to characterize 3-dimensional trans-Sasakian manifolds of type (alpha, beta) admitting *-Ricci solitons and *-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 *-Ricci soliton reduces to a beta-Kenmotsu manifold and admitting a beta-gradient Ricci soliton is either flat or *-Einstein or it becomes a beta-Kenmotsu manifold. Also an illustrative example is presented to verify our results.