On normal curves and their characterizations in Lorentzian n-space

Abstract

This paper deals with the generalization of null and non-null normal curves in Lorentzian n -space E1n. We reveal necessary and sufficient condition for a curve to be a normal curve in Lorentzian n -space E1n. We obtain the relationship between the curvatures for any arclength parametrized curve to be congruent to a normal curve in E1n. Moreover, we give differential equations by introducing a differentiable function f(s) which can be solved explicitly for a curve to be congruent to a normal curve.