Structure Functions of Cone Curves in $\mathbb{E}_2^3$ and $\mathbb{E}_2^4$

Abstract

This paper studies cone curves by establishing structure functions. The curvature functions of spacelike and timelike cone curves are expressed in the form of structure functions and the relationship between the defined structure functions is obtined. In addition, some characters and structures for cone curves in $\mathbb{E}_2^3$ and $ \mathbb{E}_2^4$ are discussed. Finally, we give some examples.