Article ID Journal Published Year Pages File Type
4606275 Differential Geometry and its Applications 2011 8 Pages PDF
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, it 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.

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Physical Sciences and Engineering Mathematics Analysis
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