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arXiv · 1805.08491

Indefinite Einstein metrics on nice Lie groups

Diego Conti·Federico A. Rossi
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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 $\geq 8$.

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Diego Conti, Federico A. Rossi. 2018-05-22. Indefinite Einstein metrics on nice Lie groups. https://doi.org/10.1515/forum-2020-0049

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