Sectional curvature and structure functions of a two-dimensional Lorentzian manifold

TL;DR

This paper derives a formula for sectional curvature on any two-dimensional Lorentzian manifold, enhancing understanding of its geometric structure.

Contribution

It provides a new explicit formula for sectional curvature in two-dimensional Lorentzian geometry, which was previously not well-characterized.

Findings

Derived a general formula for sectional curvature

Applied the formula to specific Lorentzian manifolds

Enhanced understanding of 2D Lorentzian geometry

Abstract

In this note we obtain a formula for the sectional curvature on an arbitrary two-dimensional smooth manifold $M$ equipped with a Lorentzian metric $g$.