On Lorentzian two-symmetric manifolds of dimension four

TL;DR

This paper investigates the curvature characteristics of four-dimensional Lorentzian manifolds with two-symmetry, exploring Einstein-like metrics, Ricci solitons, and homogeneity to understand their geometric structure.

Contribution

It provides a detailed analysis of two-symmetric Lorentzian manifolds, introducing new insights into their curvature and metric properties.

Findings

Characterization of curvature properties of these manifolds

Existence conditions for Einstein-like metrics and Ricci solitons

Classification results for homogeneous two-symmetric Lorentzian manifolds

Abstract

We study curvature properties of four-dimensional Lorentzian manifold with two-symmetry property. We then consider Einstein-like metrics, Ricci solitons and homogeneity over these spaces.