Isotropic Curves and Their Characterizations in Complex Space C4

In this study, we investigate the classical differential geometry of isotropic curves in the complex space C4. We examine the constant breadth of isotropic curves and obtain some results regarding these isotropic curves. We express some characterizations of these curves via the E. Cartan derivative formula. We also indicate that the isotropic vector of these curves and pseudo curvature satisfy a third order vector differential equation with variable coefficients. We study this differential equation in some special cases. We dene evolute and involute of the isotropic curve and express some characterizations of these curves in terms of E. Cartan equations. The isotropic rectifying curve and isotropic helix are characterized in C4. Finally, we present the conditions for an isotropic curve to be an isotropic helix.