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 ≥8geq 8.

Conti, D., Rossi, F. (2020). Indefinite Einstein metrics on nice Lie groups. FORUM MATHEMATICUM, 32(6), 1599-1619 [10.1515/forum-2020-0049].

Indefinite Einstein metrics on nice Lie groups

Conti D.;Rossi F. A.
2020

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 ≥8geq 8.
Articolo in rivista - Articolo scientifico
Einstein pseudoriemannian metrics; nice Lie algebras; nilpotent Lie groups;
English
2020
32
6
1599
1619
reserved
Conti, D., Rossi, F. (2020). Indefinite Einstein metrics on nice Lie groups. FORUM MATHEMATICUM, 32(6), 1599-1619 [10.1515/forum-2020-0049].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/282927
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