Affiliation:
1. Dipartimento di Matematica e Applicazioni , Università di Milano Bicocca , via Cozzi 55, 20125 Milano , Italy
Abstract
Abstract
We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups.
On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for which the nice basis is orthogonal and a more general class associated to order two permutations of the nice basis.
We obtain classifications in dimension 8 and, under the assumption that the root matrix is surjective, dimension 9; moreover, we prove that Einstein nilpotent Lie groups of nonzero scalar curvature exist in every dimension
≥
8
{\geq 8}
.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Subject
Applied Mathematics,General Mathematics
Cited by
5 articles.
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