Rigidity results for quotient almost Yamabe solitons

TL;DR

This paper studies the structure of quotient almost Yamabe solitons, providing conditions under which they are trivial or spherical, and characterizes certain noncompact cases with specific Ricci and potential function conditions.

Contribution

It introduces quotient almost Yamabe solitons, extending previous concepts, and establishes conditions for their triviality or spherical isometry, along with characterizations of noncompact cases.

Findings

Compact quotient almost Yamabe solitons are either trivial or isometric to spheres.

Noncompact quotient gradient almost Yamabe solitons are characterized under Ricci and potential function conditions.

Provides new insights into the structure of solutions to the Yamabe flow.

Abstract

In this paper we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call quotient almost Yamabe solitons because they extend quite naturally those called quotient Yamabe solitons. We then present sufficient conditions for a compact quotient almost Yamabe soliton to be either trivial or isometric with an Euclidean sphere. We also characterize noncompact quotient gradient almost Yamabe solitons satisfying certain conditions on both its Ricci tensor and potential function.