Generalized Quasi Yamabe Gradient Solitons and Applications

TL;DR

This paper investigates generalized quasi Yamabe gradient solitons on warped product manifolds, establishing conditions for their existence and exploring applications in Lorentzian and neutral geometries, including specific spacetime models.

Contribution

It provides necessary and sufficient conditions for generalized quasi Yamabe gradient solitons on warped products and demonstrates their existence in important spacetime geometries.

Findings

Existence of non-trivial gradient Yamabe solitons on generalized Robertson-Walker spacetimes

Existence on standard static spacetimes

Existence on Walker manifolds

Abstract

The purpose of this article is to study generalized quasi Yamabe gradient solitons on warped product manifolds. First, we obtain some necessary and sufficient conditions for the existence of generalized quasi Yamabe gradient solitons equipped with the warped product structure. Then we study three important applications in the Lorentzian and the neutral settings for the particular class, called as gradient Yamabe soliton: We proved the existence of the non-trivial gradient Yamabe soliton on generalized Robertson-Walker spacetimes, standard static spacetimes and Walker manifolds.