Journal
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
Volume 29, Issue 1, Pages 93-100Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.difgeo.2010.11.003
Keywords
Quasi-Einstein metrics; Rigidity
Categories
Funding
- NSF [DMS-0505733]
- Direct For Mathematical & Physical Scien [0806016] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0806016] Funding Source: National Science Foundation
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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 Kahler quasi-Einstein metrics. (C) 2010 Elsevier B.V. All rights reserved.
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