Rigidity of Quasi-Einstein Metrics

2008/05/20 by Jeffrey Case, Case, Jeffrey, Yujen Shu +3 · 12 citations
Mathematics · #53C24 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:53C24 #msc:53C25

paper · pdf · doi:10.48550/arxiv.0805.3132

10 pages

arxiv created 2008/05/20 · arxiv updated 2010/12/16

Abstract

We call a metric quasi-Einstein if the m-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of Einstein metrics, which contains gradient Ricci solitons and is also closely related to the construction of the warped product Einstein metrics. We study properties of quasi-Einstein metrics and prove several rigidity results. We also give a splitting theorem for some Kähler quasi-Einstein metrics.

Cited by

• Remarks on potential functions of noncompact quasi-Einstein manifolds
• Quasi-Einstein manifolds with Harmonic Weyl curvature
• On Compact Quasi-Einstein Metrics of Constant Scalar Curvature
• Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature
• Quasi-Einstein Metrics and a curvature identity associated with the Ricci flow
• Remark on a geometric inequality for closed hypersurfaces in weighted manifolds
• Characterization of generalized quasi-Einstein manifolds and modified gravity
• A nongradient Ricci almost soliton
• On Nilpotent and Solvable Quasi-Einstein Manifolds
• Rigidity of complete non-compact generalized m-quasi-Einstein manifolds
• A Conformal Quasi Einstein Characterization Of The Round Sphere
• Quasi-Einstein structures and Hitchin's equations

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