论文标题
坡度$ρ$ -IENSTEIN SOLITONS的定理
Splitting theorem of Gradient $ρ$-Einstein solitons
论文作者
论文摘要
在本文中，我们已经证明了与Bakry-émery曲率从下方界定的歧管的距离功能的加权拉普拉斯比较。接下来，我们已经证明，在RICCI曲率上具有有界积分条件的梯度$ρ$ -Einstein soliton将线条从等法上分离。此外，使用此结果，我们已经在梯度$ρ$ -Einstein Soliton的标态曲率上建立了一些有界条件。
In this paper, we have proved a weighted Laplacian comparison of distance function for manifolds with Bakry-Émery curvature bounded from below. Next, we have shown that a gradient $ρ$-Einstein soliton with a bounded integral condition on Ricci curvature splits off a line isometrically. Moreover, using this result, we have established some boundedness conditions on scalar curvature of gradient $ρ$-Einstein soliton.
