Rigidity of quasi-Einstein metrics

Jeffrey Case, Yu Jen Shu, Guofang Wei

Research output: Contribution to journalArticlepeer-review

111 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)93-100
Number of pages8
JournalDifferential Geometry and its Application
Volume29
Issue number1
DOIs
StatePublished - Feb 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics

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