Rigidity of Quasi-Einstein Metrics

2008/05/20 by Case, Jeffrey, Shu, Yujen, Wei, Guofang · 9 citations
#53C24 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.0805.3132

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 assoicated to 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

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• Quasi-Einstein Metrics and a curvature identity assoicated to the Ricci flow
• A Characterization of Quasi-Einstein Metrics
• Smooth metric measure spaces and quasi-Einstein metrics
• Non-trivial m-quasi-Einstein metrics on simple Lie groups
• Rigidity of quasi-Einstein metrics: The incompressible case