Ricci-flat and Einstein pseudoriemannian nilmanifolds

Abstract

This is partly an expository paper, where the authors’ work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of a diagonal Einstein metric on a nice nilpotent Lie group. Classifications of special classes of Ricci-˛at metrics on nilpotent Lie groups of dimension [eight.tf] are obtained. Some related open questions are presented.

Keywords

• einstein pseudoriemannian metrics
• nilpotent lie groups
• nice lie algebras
• 53c25
• 53c50
• 53c30
• 22e25