Some Characterizations of Quasi Yamabe solitons

TL;DR

This paper investigates properties of quasi Yamabe solitons, establishing conditions on the potential vector field and scalar curvature, and characterizing when they reduce to Yamabe solitons, especially under finiteness and curvature constraints.

Contribution

It provides new criteria for potential vector fields in quasi Yamabe solitons and characterizes when such solitons simplify to Yamabe solitons based on curvature and volume conditions.

Findings

Potential vector field with finite global norm implies constant scalar curvature.

Necessary condition for compact quasi Yamabe solitons derived.

Finite volume and non-triviality lead to scalar curvature being constant.

Abstract

In this article, we have proved some results in connection with the potential vector field having finite global norm in quasi Yamabe soliton. We have derived some criteria in particular for the potential vector field on the non-positive Ricci curvature of the quasi Yamabe soliton. Also, a necessary condition for a compact quasi Yamabe soliton has been formulated. We further showed that if the potential vector field has a finite global norm in a complete non-trivial, non-compact quasi Yamabe soliton with finite volume, then the scalar curvature becomes constant and the soliton reduces to a Yamabe soliton.