The equi-affine and Frenet curvatures of curves in pseudo-Riemannian 2-manifolds

TL;DR

This paper establishes a relationship between equi-affine and Frenet curvatures for nondegenerate curves in pseudo-Riemannian 2-manifolds, providing a new way to analyze their geometric properties.

Contribution

It derives an explicit formula connecting equi-affine curvature to Frenet curvature in pseudo-Riemannian 2-manifolds, extending classical results to a broader setting.

Findings

Derived formula linking equi-affine and Frenet curvatures

Applicable to curves in pseudo-Riemannian 2-manifolds

Enhances understanding of curve geometry in indefinite metrics

Abstract

For an arbitrary nondegenerate curve in a pseudo-Riemann\-ian (including Riemannian) 2-manifold, we express the equi-affine curvature with the help of the Frenet (geodesic) curvature of this curve.