Rigidity of Quasi-Einstein Metrics
Differential Geometry
2010-12-16 v1 Metric Geometry
Abstract
We call a metric quasi-Einstein if the -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.
Keywords
Cite
@article{arxiv.0805.3132,
title = {Rigidity of Quasi-Einstein Metrics},
author = {Jeffrey Case and Yujen Shu and Guofang Wei},
journal= {arXiv preprint arXiv:0805.3132},
year = {2010}
}
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10 pages