Universal Walker metrics

TL;DR

This paper introduces new four-dimensional neutral signature Walker spaces that are universal, expanding the class of known universal spaces with unique properties not found in other signatures.

Contribution

It presents the first examples of universal Walker spaces in four-dimensional neutral signature, highlighting their unique characteristics and expanding the understanding of universal geometric structures.

Findings

Examples of four-dimensional neutral signature universal Walker spaces.

These spaces are unique to the neutral signature and have no counterparts in other signatures.

The spaces provide a new class of universal geometries in differential geometry.

Abstract

We consider four dimensional spaces of neutral signature and give examples of universal spaces of Walker type. These spaces have no analogue in other signatures in four dimensions and provide with a new class of spaces being universal.