A non-Standard Indefinite Einstein Solvmanifold

TL;DR

This paper presents an example of an indefinite Einstein metric on a solvmanifold that is non-standard, with a nondegenerate restriction on its nilradical, expanding the understanding of Einstein metrics in indefinite geometry.

Contribution

It introduces a novel example of a non-standard indefinite Einstein solvmanifold with a nondegenerate nilradical restriction.

Findings

Provides the first known example of such a non-standard indefinite Einstein solvmanifold.

Shows the existence of Einstein metrics with nondegenerate nilradical restrictions.

Enhances the classification of Einstein metrics on solvmanifolds.

Abstract

We describe an example of an indefinite invariant Einstein metric on a solvmanifold which is not standard, and whose restriction on the nilradical is nondegenerate.