Scalar curvature estimation of Generalized Ricci-Yamabe solitons

TL;DR

This paper investigates the properties of generalized gradient Ricci-Yamabe solitons, providing conditions for constant scalar curvature, curvature estimates, and characterizations of when they reduce to Einstein manifolds.

Contribution

It offers new characterizations and conditions for generalized Ricci-Yamabe solitons, including scalar curvature constancy and reduction to Einstein manifolds.

Findings

Scalar curvature becomes constant under certain conditions

Ricci curvature estimation is derived

Ricci-Yamabe soliton reduces to Einstein manifold with concircular potential

Abstract

This paper is concerned with the study of generalized gradient Ricci-Yamabe solitons. We characterize the compact generalized gradient Ricci-Yamabe soliton and find certain conditions under which the scalar curvature becomes constant. The estimation of Ricci curvature is deduced and also an isometry theorem is found in gradient Ricci-Yamabe soliton satisfying a finite weighted Dirichlet integral. Further, it is proved that a Ricci-Yamabe soliton reduces to an Einstein manifold when the potential vector field becomes concircular. Moreover, the eigenvalue and the corresponding eigenspace of the Ricci operator are also discussed in case of a Ricci-Yamabe soliton with concircular potential vector field.