Left-invariant pseudo-Riemannian metrics on four-dimensional Lie groups with zero Schouten-Weyl tensor

TL;DR

This paper classifies four-dimensional Lie groups with left-invariant pseudo-Riemannian metrics that have a zero Schouten-Weyl tensor, providing a comprehensive understanding of their structure through algebraic constants.

Contribution

It offers a complete classification of such Lie groups based on their Lie algebra structure constants, a novel result in this area.

Findings

Complete classification of four-dimensional Lie groups with the specified metrics

Explicit description of structure constants for these Lie groups

Advancement in understanding geometric properties of pseudo-Riemannian Lie groups

Abstract

In the presented paper left-invariant pseudo-Riemannian metrics on four-dimensional Lie groups with zero Schouten-Weyl tensor are investigated. The complete classification of these metric Lie groups is obtained in terms of the structure constants of corresponding Lie algebras.