On the classification of warped product Einstein metrics

Chenxu He, Peter Petersen, William Wylie

Research output: Contribution to journalArticle

45 Scopus citations

Abstract

In this paper we take the perspective introduced by Case-Shu-Wei of studying warped product Einstein metrics through the equation for the Ricci curvature of the base space. They call this equation on the base the m-quasi Einstein equation, but we will also call it the (λ, n + m)-Einstein equation. In this paper we extend the work of Case-Shu-Wei and some earlier work of Kim-Kim to allow the base to have non-empty boundary. This is a natural case to consider since a manifold without boundary often occurs as a warped product over a manifold with boundary, and in this case we get some interesting new canonical examples. We also derive some new formulas involving curvatures that are analogous to those for the gradient Ricci solitons. As an application, we characterize warped product Einstein metrics when the base is locally conformally flat.

Original languageEnglish (US)
Pages (from-to)271-311
Number of pages41
JournalCommunications in Analysis and Geometry
Volume20
Issue number2
DOIs
StatePublished - Mar 2012

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ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

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