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arXiv · 2206.13825

Pseudo-K\"ahler and pseudo-Sasaki structures on Einstein solvmanifolds

Diego Conti·Federico A. Rossi·Romeo Segnan Dalmasso
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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 $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $2n+3$, which are in one-to-one correspondence with pseudo-K\"ahler nilpotent Lie algebras of dimension $2n$ endowed with a compatible derivation, in a suitable sense. We characterize the pseudo-K\"ahler structures and derivations giving rise to Sasaki-Einstein metrics. We classify $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $\leq 7$ and those whose pseudo-K\"ahler reduction is an abelian Lie algebra. The Einstein metrics we obtain are standard, but not of pseudo-Iwasawa type.

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Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso. 2022-06-28. Pseudo-K\"ahler and pseudo-Sasaki structures on Einstein solvmanifolds. https://doi.org/10.1007/s10455-023-09894-0

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