On Sectional Curvature Operator of 3-dimensional Locally Homogeneous Lorentzian Manifolds

TL;DR

This paper classifies the possible forms of the sectional curvature operator on three-dimensional locally homogeneous Lorentzian manifolds, providing a comprehensive understanding of their curvature properties.

Contribution

It determines the admissible forms of the sectional curvature operator specifically for three-dimensional locally homogeneous Lorentzian manifolds, a novel classification in this context.

Findings

Complete classification of sectional curvature operators

Identification of possible curvature forms in Lorentzian geometry

Enhanced understanding of curvature structures in homogeneous manifolds

Abstract

The main purpose of this paper is to determine the admissible forms of the sectional curvature operator on a three-dimensional locally homogeneous Lorentzian manifolds.