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arXiv · 2003.05234

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

Absos Ali Shaikh·Chandan Kumar Mondal·Prosenjit Mandal
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Abstract

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

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Absos Ali Shaikh, Chandan Kumar Mondal, Prosenjit Mandal. 2020-03-11. Compact gradient $\rho$-Einstein soliton is isometric to the Euclidean sphere. https://arxiv.org/abs/2003.05234

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