Rigidity and Triviality of Gradient r -Almost Newton-Ricci-Yamabe Solitons

Mohd Danish Siddiqi () and Fatemah Mofarreh
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Mohd Danish Siddiqi: Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 4512, Saudi Arabia
Fatemah Mofarreh: Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia

Mathematics, 2024, vol. 12, issue 20, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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