论文标题
局部均质的非梯度准伊因斯坦3个manifolds
Locally Homogeneous Non-gradient Quasi-Einstein 3-Manifolds
论文作者
论文摘要
在本文中，我们将紧凑的本地均质非梯度$ m $ -quasi Einstein 3-manifolds分类。在此过程中，我们证明，鉴于任何一个是$ m $ -quasi Einstein的谎言组的紧凑型商，潜在的矢量场$ x $必须保持不变和杀戮。我们还对非平凡的$ m $ quasi爱因斯坦指标进行了分类，这些指标是两个爱因斯坦指标的产品的紧凑商。我们还表明，$ s^1 $是任何维度的唯一紧凑型歧管，它承认非试图$ m $ -quasi Einstein和Einstein的度量。
In this paper, we classify the compact locally homogeneous non-gradient $m$-quasi Einstein 3-manifolds. Along the way, we prove that given a compact quotient of a Lie group of any dimension that is $m$-quasi Einstein, the potential vector field $X$ must be left invariant and Killing. We also classify the nontrivial $m$-quasi Einstein metrics that are a compact quotient of be the product of two Einstein metrics. We also show that $S^1$ is the only compact manifold of any dimension which admits a metric which is nontrivially $m$-quasi Einstein and Einstein.
