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

Autor:	Shaikh, Absos Ali, Mondal, Chandan Kumar, Mandal, Prosenjit
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry 53C20 53C21 53C44
Druh dokumentu:	Working Paper
Popis:	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. Comment: 6 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.05234 Zobrazit plný text záznamu View this record from Arxiv