New Special Einstein Pseudo-Riemannian Metrics on Solvable Lie Algebras

Abstract

We exhibit a concrete procedure to construct Einstein pseudo-Kähler and para-Kähler metrics on solvable Lie algebras. We apply this method to classify all the rank-one pseudo-Iwasawa extensions of type-(Nil4) nilsoliton in low dimension. We prove that such metrics exists on the rank-one pseudo-Iwasawa extension of the generalized Heisenberg Lie algebra. Further ideas and suggestions to produce more special Einstein pseudo-Riemannian metrics are exposed.

arXiv comment23 pages, 3 tables, 1 figure

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