Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons

Chenxu He, Peter Petersen, William Wylie

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

In this paper we consider connections between Ricci solitons and Einstein metrics on homogeneous spaces. We show that a semi-algebraic Ricci soliton admits an Einstein one-dimensional extension if the soliton derivation can be chosen to be normal. Using our previous work on warped product Einstein metrics, we show that every normal semi-algebraic Ricci soliton also admits a k-dimensional Einstein extension for any k ≥ 2. We also prove converse theorems for these constructions and some geometric and topological structure results for homogeneous warped product Einstein metrics. In the appendix we give an alternative approach to semi-algebraic Ricci solitons which naturally leads to a definition of semi-algebraic Ricci solitons in the non-homogeneous setting.

Original languageEnglish (US)
Pages (from-to)217-245
Number of pages29
JournalJournal fur die Reine und Angewandte Mathematik
Volume2015
Issue number707
DOIs
StatePublished - Oct 1 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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