Rigidity of Quasi-Einstein Metrics

Details Rigidity of Quasi-Einstein Metrics Rigidity of Quasi-Einstein Metrics

2008-05-20

arxiv.org/abs/0805.3132v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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 K\"ahler quasi-Einstein metrics.

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