Pr EXPLICIT CHARACTERIZATION OF THE RADIUS OF CURVES LYING IN A SURFACE OF $\mathbb{E}^3$ OR $\mathbb{E}^3_1$

Abstract

In this paper we show that the differential equation characterizing a curve lying in an oriented surface $\mathbb{E}^3$ or $\mathbb{E}^3_1$ allows two express the radius of the curvature of the curve in terms of its torsions.