Spacelike normal curves in Minkowski space $Bbb{E}_1^3$

Abstract

In the Euclidean space $Bbb{E}^3$, it is well known that normal curves, i.e., curves with position vector always lying in their normal plane, are spherical curves [3]. Necessary and sufficient conditions for a curve to be a spherical curve in Euclidean 3-space are given in [10] and [11]. In this paper, we give some characterizations of spacelike normals curves with spacelike, timelike or null principal normal in the Minkowski 3-space $Bbb{E}_1^3$.