Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022

Federico A. Rossi [a]

New special Einstein pseudo-Riemannian metrics on solvable Lie algebras

Pages: 449-479
Received: 1 December 2021
Accepted in revised form: 28 March 2022
Mathematics Subject Classification: 53C50, 53C25, 53C30, 22E25, 32M10.
Keywords: Einstein metrics, nilsolitons, solvable Lie algebras, pseudo-Riemannian homogeneous metrics, complex structures, para-complex structures.
Author address:
[a]: Università degli Studi di Perugia, Dipartimento di Matematica e Informatica, Perugia, Italy

This research was partially supported by GNSAGA of INdAM and the Young Talents Award of Università degli Studi di Milano-Bicocca joint with Accademia Nazionale dei Lincei

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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 exist 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.

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