Locally homogeneous non-gradient quasi-Einstein 3-manifolds
Locally homogeneous non-gradient quasi-Einstein 3-manifolds
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DOI：
10.1515/advgeom-2021-0036
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发表时间：
2020-09
影响因子：
0.5
通讯作者：
Alice Lim
中科院分区：
文献类型：
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作者：
Alice Lim
本文对紧致局部齐次非梯度m-拟Einstein三维流形进行了分类。沿着的方式，我们还证明了，给定一个紧商的李群的任何维是m-准爱因斯坦，潜在的向量场X必须是左不变的和Killing。我们还分类的非平凡的m-拟爱因斯坦度量是一个紧凑的商的产品的两个爱因斯坦度量。我们还表明，S1是唯一的紧致流形的任何维度，它承认一个度量，这是非平凡的m-拟爱因斯坦和爱因斯坦。
Abstract In this paper, we classify the compact locally homogeneous non-gradient m-quasi Einstein 3- manifolds. Along the way, we also 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 the product of two Einstein metrics. We also show that S1 is the only compact manifold of any dimension which admits a metric which is nontrivially m-quasi Einstein and Einstein.