局部齐次非梯度拟爱因斯坦3-流形

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2020-09-01 DOI:10.1515/advgeom-2021-0036

Alice Lim

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引用次数: 4

摘要

摘要本文对紧致局部齐次非梯度m-拟Einstein 3-流形进行了分类。在此过程中，我们还证明了给定任意维度的李群的紧致商为m-拟爱因斯坦，势向量场X必须保持不变且为Killing。我们还对非平凡m-拟爱因斯坦度量进行了分类，它是两个爱因斯坦度量乘积的紧致商。我们还证明了S1是任何维度上唯一允许度量的紧致流形，该度量是非平凡的m-拟爱因斯坦和爱因斯坦。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Locally homogeneous non-gradient quasi-Einstein 3-manifolds

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.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.