Four-dimensional pp-wave Lie groups and harmonic curvature

TL;DR

This paper classifies all four-dimensional Lie groups with harmonic curvature and provides a detailed description of four-dimensional pp-wave Lie groups, advancing understanding of their geometric structures.

Contribution

It offers a complete classification of four-dimensional Lie groups with harmonic curvature and characterizes four-dimensional pp-wave Lie groups.

Findings

Identified all four-dimensional Lie groups with harmonic curvature.

Provided a detailed description of four-dimensional pp-wave Lie groups.

Enhanced understanding of the geometric properties of these groups.

Abstract

We determine all four-dimensional Lie groups which have harmonic curvature. As a consequence, a description of four-dimensional pp-wave Lie groups is obtained.