Conformally flat pseudo Riemannian Homogeneous Ricci Solitons 4 spaces

TL;DR

This paper classifies four-dimensional conformally flat homogeneous pseudo Riemannian Ricci solitons based on Ricci operator forms, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete classification of 4D conformally flat homogeneous Ricci solitons using Ricci operator Seger types, a novel systematic approach.

Findings

Full classification of Ricci solitons in 4D conformally flat homogeneous pseudo Riemannian manifolds.

Identification of Ricci operator forms (Seger types) relevant to these solitons.

Clarification of the geometric structure of these manifolds.

Abstract

We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat homogeneous Ricci solitons.