On the Involute-Evolute of the Pseudonull Curve in Minkowski 3-Space

Abstract

We have generalized the involute and evolute curves of the pseudonull curves $\alpha$ in ${𝔼}_{\mathrm{1}}^{\mathrm{3}}$; that is, $\alpha$ is a spacelike curve with a null principal normal. Firstly, we have shown that there is no involute of the pseudonull curves $\alpha$ in ${𝔼}_{\mathrm{1}}^{\mathrm{3}}$. Secondly, we have found relationships between the evolute curve β and the pseudonull curve $\alpha$ in ${𝔼}_{\mathrm{1}}^{\mathrm{3}}$. Finally, some examples concerning these relations are given.