Immersion of gradient almost Yamabe solitons into warped product manifolds

TL;DR

This paper explores the geometry of gradient almost Yamabe solitons immersed in warped product manifolds, providing rigidity results, existence conditions, and classifications for special types of solitons.

Contribution

It introduces new geometric rigidity results, existence criteria, and classifications for gradient almost Yamabe solitons in warped product manifolds.

Findings

Rigidity results for compact solitons under curvature conditions

Conditions for existence of totally geodesic, umbilical, and minimal solitons

Classification of rotational gradient almost Yamabe solitons in specific warped products

Abstract

The purpose of this article is to study the geometry of gradient almost Yamabe solitons immersed into warped product manifolds $I\times_{f}M^{n}$ whose potential is given by the height function from the immersion. First, we present some geometric rigidity on compact solitons due to a curvature condition on the warped product manifold. In the sequel, we investigate conditions for the existence of totally geodesic, totally umbilical and minimal solitons. Furthermore, in the scope of constant angle immersions, a classification of rotational gradient almost Yamabe soliton immersed into $\mathbb{R}\times_{f}\mathbb{R}^{n}$ is also made.