Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Q\varphi=\varphi Q

TL;DR

This paper explores quasi Yamabe solitons on 3D contact metric manifolds satisfying a specific curvature condition, establishing conditions for the soliton vector field, scalar curvature, and manifold structure, including Sasakian and flat cases.

Contribution

It introduces the study of quasi Yamabe solitons on 3D contact metric manifolds with Qφ=φQ and characterizes their properties under certain conditions.

Findings

V is a constant multiple of ξ when V is collinear with ξ.

Scalar curvature is constant on the manifold.

If the manifold is compact, it is either flat or the soliton is trivial.

Abstract

In this paper we initiate the study of quasi Yamabe soliton on 3-dimensional contact metric manifold with Q\varphi=\varphi Q and prove that if a 3-dimensional contact metric manifold M such that Q\varphi=\varphi Q admits a quasi Yamabe soliton with non-zero soliton vector field V being point-wise collinear with the Reeb vector field {\xi}, then V is a constant multiple of {\xi}, the scalar curvature is constant and the manifold is Sasakian. Moreover, V is Killing. Finally, we prove that if M is a 3-dimensional compact contact metric manifold such that Q\varphi=\varphi Q endowed with a quasi Yamabe soliton, then either M is flat or soliton is trivial.