Serret-Frenet Equations in Minkowski Space

Abstract

In this paper we established the Serret-Frenet equations in Minkowski space. These equations originally formulated in Euclidean space in R³, constitute a beautiful set of vector differential equations which contains all intrinsic properties of parameterized curve. From the local theory of curves in R³ states that a curve lies in a plane if and only if its torsion vanishes, which gives us clear geometrical insight in the notion of torsion. This theorem has two counterparts in Minkowski space that has been focused.