Published Paper
Inserted: 1 sep 2024
Last Updated: 18 may 2025
Journal: Transformation Groups
Year: 2024
Doi: 10.1007/s00031-024-09864-1
Abstract:
We construct indefinite Einstein solvmanifolds that are standard, but not of pseudo-Iwasawa type. Thus, the underlying Lie algebras take the form $\mathfrak{g}\rtimes_D\mathbb{R}$, where $\mathfrak{g}$ is a nilpotent Lie algebra and $D$ is a nonsymmetric derivation. Considering nonsymmetric derivations has the consequence that $\mathfrak{g}$ is not a nilsoliton, but satisfies a more general condition. Our construction is based on the notion of nondiagonal triple on a nice diagram. We present an algorithm to classify nondiagonal triples and the associated Einstein metrics. With the use of a computer, we obtain all solutions up to dimension $5$, and all solutions in dimension $\leq9$ that satisfy an additional technical restriction. By comparing curvatures, we show that the Einstein solvmanifolds of dimension $\leq 5$ that we obtain by our construction are not isometric to a standard extension of a nilsoliton.
Tags:
PRIN2022-GSFT