A note on warped product almost quasi-Yamabe solitons

TL;DR

This paper studies almost quasi-Yamabe solitons on Riemannian manifolds, deriving formulas and conditions that relate the geometry of the manifold and warped products, with implications for scalar curvature.

Contribution

It introduces new conditions for gradient almost quasi-Yamabe solitons on warped products and derives a Bochner-type formula in this context.

Findings

Manifolds with almost quasi-Yamabe solitons have constant scalar curvature under certain conditions.

Derived a Bochner-type formula for gradient cases.

Established conditions linking base and warped product manifolds for solitons.

Abstract

We consider almost quasi-Yamabe solitons in Riemannian manifolds, derive a Bochner-type formula in the gradient case and prove that under certain assumptions, the manifold is of constant scalar curvature. We also provide necessary and sufficient conditions for a gradient almost quasi-Yamabe soliton on the base manifold to induce a gradient almost quasi-Yamabe soliton on the warped product manifold.