The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of z-standard Sasaki solvable Lie algebras of dimension 2 n+ 3 , which are in one-to-one correspondence with pseudo-Kähler nilpotent Lie algebras of dimension 2n endowed with a compatible derivation, in a suitable sense. We characterize the pseudo-Kähler structures and derivations giving rise to Sasaki–Einstein metrics. We classify z-standard Sasaki solvable Lie algebras of dimension ≤ 7 and those whose pseudo-Kähler reduction is an abelian Lie algebra. The Einstein metrics we obtain are standard, but not of pseudo-Iwasawa type.

Conti, D., Rossi, F., Segnan Dalmasso, R. (2023). Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 63(3) [10.1007/s10455-023-09894-0].

Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds

Rossi, FA
;
Segnan Dalmasso, R
2023

Abstract

The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of z-standard Sasaki solvable Lie algebras of dimension 2 n+ 3 , which are in one-to-one correspondence with pseudo-Kähler nilpotent Lie algebras of dimension 2n endowed with a compatible derivation, in a suitable sense. We characterize the pseudo-Kähler structures and derivations giving rise to Sasaki–Einstein metrics. We classify z-standard Sasaki solvable Lie algebras of dimension ≤ 7 and those whose pseudo-Kähler reduction is an abelian Lie algebra. The Einstein metrics we obtain are standard, but not of pseudo-Iwasawa type.
Articolo in rivista - Articolo scientifico
Einstein; Indefinite metric; Sasaki; Solvable Lie group; Standard Lie algebra;
English
24-apr-2023
2023
63
3
25
open
Conti, D., Rossi, F., Segnan Dalmasso, R. (2023). Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 63(3) [10.1007/s10455-023-09894-0].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/473179
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