Warped product Einstein metrics over spaces with constant scalar curvature

Chenxu He, Peter Petersen, William Wylie

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the base is three dimensional and the dimension of the fiber is greater than one we show that the space is always rigid. We also exhibit examples of solvable four dimensional Lie groups that can be used as the base space of non-rigid warped product Einstein metrics showing that the result is not true in dimension greater than three. We also give some further natural curvature conditions that characterize the rigid examples in higher dimensions.

Original languageEnglish (US)
Pages (from-to)159-190
Number of pages32
JournalAsian Journal of Mathematics
Volume18
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Einstein manifolds
  • Ricci solitons
  • Rigidity
  • Solvable lie groups
  • Warped products

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Warped product Einstein metrics over spaces with constant scalar curvature'. Together they form a unique fingerprint.

Cite this