New Parametrization of Bertrand Partner D-curves in $\mathbb{E}^{3}$

Abstract

We define and study a new parametrization of a Bertrand partner D-curve \{$\alpha$,$\alpha^{*}$\} in Euclidean 3-space by not taking Darboux frame element $g^{*}$ of Bertrand partner D-curve $\alpha^{*}$ parallel to $\overrightarrow{\alpha \alpha^{*}}$. We obtain a necessary and sufficient condition for a curve to be such type of Bertrand D-curves. Also, we obtain a characterization of a new parametrization of asymptotic Bertrand D-curves and provide an example.