On the structure of almost Yamabe solitons

TL;DR

This paper explores the geometric structure of almost Yamabe solitons, identifying conditions under which they become trivial and revealing a local warped product structure when the vector field is closed.

Contribution

It provides new conditions for triviality of almost Yamabe solitons and generalizes existing results by establishing a local warped product structure for solitons with closed vector fields.

Findings

Conditions for triviality of almost Yamabe solitons.

Existence of local warped product structure with closed vector fields.

Generalization of previous results in the literature.

Abstract

In this paper, we study structures of almost Yamabe solitons which are not necessarily gradient. First, we investigate conditions that both compact and noncompact almost Yamabe solitons become trivial solitons which means the given vector field is a Killing vector field. Second, we show that an almost Yamabe soliton whose vector field is closed admits a local warped product structure with a one-dimensional base. This result can be considered as a generalization of a result in \cite{c-s-z} and \cite{c-m-m}