On the Killing property of the defining vector field for an almost Yamabe soliton

TL;DR

This paper explores conditions under which the defining vector field of an almost Yamabe soliton is a Killing vector field on both compact and non-compact Riemannian manifolds, extending previous results.

Contribution

It establishes new sufficient conditions for the Killing property of the defining vector field in almost Yamabe solitons on various types of manifolds.

Findings

The conformal vector field is Killing under certain conditions on compact manifolds.

The Killing property holds for complete non-compact manifolds with specific assumptions.

Results extend the understanding of symmetries in almost Yamabe solitons.

Abstract

In this paper, we first investigate almost Yamabe solitons on compact Riemannian manifolds without boundary of dimension greater than or equal to two. We provide some sufficient conditions for which the defining conformal vector field associated to a compact almost Yamabe soliton is a Killing vector field. We then study almost Yamabe solitons on complete, non-compact Riemannian manifolds. We prove the Killing property of the defining conformal vector field associated to a complete, non-compact almost Yamabe soliton under certain conditions when the dimension is strictly greater than two.