A new parametrization of Cartan null Bertrand curve in Minkowski 3-space

Abstract

We define and study a new parametrization of a Bertrand pair $\{\alpha,\,\alpha^{*}\}$, where $\alpha$ is a Cartan null Bertrand curve and $\alpha^{*}$ is a Bertrand partner curve of $\alpha$ in Minkowski 3-space by not taking the principal normal vector of the Cartan null Bertrand curve $\alpha$ parallel to $\overrightarrow{\alpha^{*} \,\alpha}$. We characterize both cases when the curve $\alpha^{*}$ is non-null and the null Bertrand partner of the curve $\alpha$. Further, we investigate this type of Bertrand pair curve as a helix and a slant helix. Also, we provide some examples.