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Soliton-Type Equations on a Riemannian Manifold

Author

Listed:
  • Nasser Bin Turki

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
    These authors contributed equally to this work.)

  • Adara M. Blaga

    (Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timisoara, 300223 Timisoara, Romania
    These authors contributed equally to this work.)

  • Sharief Deshmukh

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

We study some particular cases of soliton-type equations on a Riemannian manifold. We give an estimation of the first nonzero eigenvalue of the Laplace operator and provide necessary and sufficient conditions for the manifold to be isometric to a sphere. Finally, we characterize trivial generalized gradient Ricci solitons.

Suggested Citation

  • Nasser Bin Turki & Adara M. Blaga & Sharief Deshmukh, 2022. "Soliton-Type Equations on a Riemannian Manifold," Mathematics, MDPI, vol. 10(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:633-:d:752505
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