Some results on $\eta$-Yamabe solitons in 3-dimensional trans-Sasakian manifold

Abstract

The object of the present paper is to study some properties of 3-dimensional trans-Sasakian manifold whose metric is $\eta$-Yamabe soliton. We have studied here some certain curvature conditions of 3-dimensional trans-Sasakian manifold admitting $\eta$-Yamabe soliton. Lastly, we construct a 3-dimensional trans-Sasakian manifold satisfying $\eta$-Yamabe soliton.