论文标题
紧凑型梯度$ρ$ -IENSTEIN SOLITON是欧几里得球的等距
Compact gradient $ρ$-Einstein soliton is isometric to the Euclidean sphere
论文作者
论文摘要
在本文中，我们研究了完整的Riemannian歧管中梯度$ρ$ -Einstein Ricci Soliton的某些方面。首先，我们已经证明了紧凑的梯度$ρ$ -IENSTEIN SOLITON是欧几里得球的等距，这表明标量曲率变得恒定。其次，我们表明，在非紧密梯度$ρ$ -Einstein soliton中，满足某些积分条件，标量曲率消失了。
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 is isometric to the Euclidean sphere by showing that the scalar curvature becomes constant. Second, we have showed that in a non-compact gradient $ρ$-Einstein soliton satisfying some integral condition, the scalar curvature vanishes.
