Locally Homogeneous Non-gradient Quasi-Einstein 3-Manifolds

2020/09/01 by Alice Lim, Lim, Alice · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.2009.00720

30 pages

arxiv created 2020/09/01 · arxiv updated 2020/09/03

Abstract

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 S¹ is the only compact manifold of any dimension which admits a metric which is nontrivially m-quasi Einstein and Einstein.

Cited by

• On Compact Quasi-Einstein Metrics of Constant Scalar Curvature
• On Nilpotent and Solvable Quasi-Einstein Manifolds

Related

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• On Compact Quasi-Einstein Metrics of Constant Scalar Curvature
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• Non-trivial m-quasi-Einstein metrics on quadratic Lie groups