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

摘要

The object of the present paper is to characterize 3-dimen-sional trans-Sasakian manifolds of type (α,β) admitting ?-Ricci solitons and ?-gradient Ricci solitons. Under certain restrictions on the smooth functions α and β, we have proved that a trans-Sasakian 3-manifold of type (α,β) admitting a ?-Ricci soliton reduces to a β-Kenmotsu mani-fold and admitting a ?-gradient Ricci soliton is either flat or ?-Einstein or it becomes a β-Kenmotsu manifold. Also an illustrative example is presented to verify our results.