Soliton-Type Equations on a Riemannian Manifold

Nasser Bin Turki, Adara M. Blaga and Sharief Deshmukh
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Nasser Bin Turki: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Adara M. Blaga: Department of Mathematics, Faculty of Mathematics and Computer Science, West University of Timisoara, 300223 Timisoara, Romania
Sharief Deshmukh: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2022, vol. 10, issue 4, 1-10

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.

Keywords: generalized gradient soliton; unit geodesic vector field (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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