Some results on {\eta}-Yamabe Solitons in 3-dimensional trans-Sasakian manifold

TL;DR

This paper investigates properties of 3-dimensional trans-Sasakian manifolds that admit {\

Contribution

It introduces new curvature conditions for 3D trans-Sasakian manifolds with {\

Findings

Identifies specific curvature conditions under which {\

Constructs an explicit example of a 3D trans-Sasakian manifold satisfying {\

Provides insights into the geometric structure of {\

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.