Mathematica Eterna
Open Access

Abstract

Spacelike Salkowski and anti-Salkowski curves with timelike principal normal in Minkowski 3-space

Ahmad T. Ali

A century ago, Salkowski [1] introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (antiSalkowski curves). Ali (2009–2010) [2], [3] adapted the definition of such curves in Minkowski 3-space and introduced an explicit parametrization of a timelike and a spacelike (with a spacelike principal normal vector) Salkowski and anti-Salkowski curves. In this paper, we introduce an explicit parametrization of a spaelike Salkowski and anti-Salkowski curves with a timelike principal normal vector in Minkowski 3-space. Moreover, we characterize them as a space curve with constant curvature or constant torsion and whose normal vector makes a constant angle with a fixed straight line.