Compact gradient $$\rho$$ ρ -Einstein soliton is isometric to the Euclidean sphere

Absos Ali Shaikh (), Chandan Kumar Mondal () and Prosenjit Mandal ()
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Absos Ali Shaikh: The University of Burdwan, Golapbag
Chandan Kumar Mondal: The University of Burdwan, Golapbag
Prosenjit Mandal: The University of Burdwan, Golapbag

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 335-339

Abstract: Abstract In this paper, we have investigated some aspects of gradient $$\rho$$ ρ -Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient $$\rho$$ ρ -Einstein soliton satisfying some curvature conditions is isometric to the Euclidean sphere by showing that the scalar curvature becomes constant. Second, we have shown that in a non-compact gradient $$\rho$$ ρ -Einstein soliton satisfying an integral condition, the scalar curvature vanishes.

Keywords: Gradient $$\rho$$ ρ -Einstein Ricci soliton; Scalar curvature; Riemannian manifold; 53C20; 53C21; 53C44 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00034-7

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