Some isotropic curves and representation in complex space $mathbb{C}^{3}$

摘要

In this paper, we give a representation formula for an iso-tropic curve with pseudo arc length parameter and define the structure function of such curves. Using the representation formula and the Frenet formula, the isotropic Bertrand curve and $k$-type isotropic helices are characterized in the 3-dimensional complex space $mathbb{C}^{3}$.