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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mohd Danish Siddiqi & Fatemah Mofarreh, 2024. "Rigidity and Triviality of Gradient r -Almost Newton-Ricci-Yamabe Solitons," Mathematics, MDPI, vol. 12(20), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3173-:d:1495907
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