On Conformally flat homogeneous Walker four-manifolds

TL;DR

This paper investigates invariant Walker structures on conformally flat four-dimensional homogeneous manifolds, classified by the Seger types of their Ricci operators, to understand their geometric properties.

Contribution

It provides a classification of invariant Walker structures on these manifolds based on Ricci operator Seger types, advancing the understanding of their geometric configurations.

Findings

Classification of Walker structures according to Ricci Seger types

Identification of geometric properties specific to each Seger type

Extension of known results in conformally flat homogeneous manifolds

Abstract

In this paper we study the invariant Walker structures over the conformally flat four-dimensional homogeneous manifolds according to the Seger types of the Ricci operator.