Rigidity and Triviality of Gradient <i>r</i>-Almost Newton-Ricci-Yamabe Solitons

Abstract

In this paper, we develop the concept of gradient r-Almost Newton-Ricci-Yamabe solitons (in brief, gradient r-ANRY solitons) immersed in a Riemannian manifold. We deduce the minimal and totally geodesic criteria for the hypersurface of a Riemannian manifold in terms of the gradient r-ANRY soliton. We also exhibit a Schur-type inequality and discuss the triviality of the gradient r-ANRY soliton in the case of a compact manifold. Finally, we demonstrate the completeness and noncompactness of the r-Newton-Ricci-Yamabe soliton on the hypersurface of the Riemannian manifold.

Keywords

• r-Almost Newton-Ricci-Yamabe soliton
• Riemannian manifold
• triviality
• Schur-type inequality