Ricci-flat and Einstein pseudoriemannian nilmanifolds
Differential Geometry
2019-05-10 v2
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-flat metrics on nilpotent Lie groups of dimension are obtained. Some related open questions are presented.
Keywords
Cite
@article{arxiv.1812.01310,
title = {Ricci-flat and Einstein pseudoriemannian nilmanifolds},
author = {Diego Conti and Federico A. Rossi},
journal= {arXiv preprint arXiv:1812.01310},
year = {2019}
}
Comments
30 pages, 1 figure. v2: added a comment on a recent example of an Einstein nilpotent Lie algebra of dimension 7; added a remark and a question concerning the characteristically nilpotent case; replaced the "\sigma-compatible" condition with the more general "\sigma-diagonal"; added 3 references