New examples of non-symmetric Einstein solvmanifolds of negative Ricci curvature

TL;DR

This paper introduces new non-symmetric Einstein solvmanifolds with negative Ricci curvature by extending Tamaru's attached solvmanifold construction to associated solvmanifolds, resulting in examples with highly nilpotent nilradicals.

Contribution

It extends the construction of Einstein solvmanifolds to associated solvmanifolds, producing new examples with high nilpotency not derived from symmetric spaces.

Findings

New Einstein solvmanifolds with high nilpotency nilradicals

Examples are geometrically distinct from symmetric spaces

Extension of Tamaru's attached solvmanifold technique

Abstract

We obtain new examples of non-symmetric Einstein solvmanifolds by combining two techniques. In \cite{T2}, H. Tamaru constructs new {\em attached} solvmanifolds, which are submanifolds of the solvmanifolds corresponding to noncompact symmetric spaces, endowed with a natural metric. Extending this construction, we apply it to {\em associated} solvmanifolds, described in \cite{GK}, obtained by modifying the algebraic structure of the solvable Lie algebras corresponding to noncompact symmetric spaces. Our new examples are Einstein solvmanifolds with nilradicals of high nilpotency, which are geometrically distinct from noncompact symmetric spaces and their submanifolds.