Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
home | mail | papers | authors | news | seminars | events | open positions | login

D. Conti - F. A. Rossi - R. Segnan Dalmasso

Pseudo-Kähler and pseudo-Sasaki Einstein solvmanifolds

created by rossi on 29 Jun 2022

[BibTeX]

preprint

Inserted: 29 jun 2022
Last Updated: 29 jun 2022

Year: 2022

ArXiv: 2206.13825 PDF

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.

Credits | Cookie policy | HTML 5 | CSS 2.1