Locally homogeneous non-gradient quasi-Einstein 3-manifolds
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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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2018 ◽
Vol 62
(4)
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pp. 912-922
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2021 ◽
pp. 2150179
1983 ◽
Vol 19
(4)
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pp. 1545-1556
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2010 ◽
Vol 07
(06)
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pp. 951-960
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