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

In this paper, we have investigated some aspects of gradient ρ -Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient ρ -Einstein soliton satisfying some curvature conditions is isometric to the Euclidean sphere by showing that the scalar curvature...

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Veröffentlicht in:	Indian journal of pure and applied mathematics 2021-06, Vol.52 (2), p.335-339
Hauptverfasser:	Shaikh, Absos Ali, Mondal, Chandan Kumar, Mandal, Prosenjit
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Sprache:	eng
Schlagworte:	Applications of Mathematics Curvature Mathematics Mathematics and Statistics Numerical Analysis Original Research Riemann manifold Solitary waves
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description	In this paper, we have investigated some aspects of gradient ρ -Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient 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 ρ -Einstein soliton satisfying an integral condition, the scalar curvature vanishes.
doi_str_mv	10.1007/s13226-021-00034-7
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title	Compact gradient ρ-Einstein soliton is isometric to the Euclidean sphere
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