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Locally homogeneous non-gradient quasi-Einstein 3-manifolds

  • Alice Lim EMAIL logo
From the journal Advances in Geometry

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.

MSC 2010: 53C25

Funding statement: This work was partially supported by NSF grant DMS-1654034.

Acknowledgements

The author would like to thank her thesis advisor, Professor William Wylie,for all of his help and support in writing this paper.

  1. Communicated by: P. Eberlein

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Received: 2020-11-03
Published Online: 2022-01-15
Published in Print: 2022-01-27

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