On a family of Einstein like Walker metrics

TL;DR

This paper investigates four-dimensional Walker manifolds with signature (2, 2), focusing on their curvature properties and characterizing those that are Einstein-like, contributing to the understanding of special pseudo-Riemannian geometries.

Contribution

It provides a characterization of Einstein-like Walker metrics of a specific form in four dimensions, advancing the classification of such geometries.

Findings

Identification of conditions for Walker metrics to be Einstein-like

Explicit characterization of a class of Walker manifolds

Enhanced understanding of curvature properties in pseudo-Riemannian geometry

Abstract

A four dimensional pseudo-Riemannian manifold of signature (2, 2) is called a Walker manifold if it admits a parallel degenerate plane field. In this paper, we study the curvature properties of such a class of four dimensional Walker manifolds. In particular, we characterize Walker metrics of a given form which are Einstein-like.