Generalization of general helices and slant helices

In this work, we use the formal de nition of k-slant helix [5] to obtain the intrinsic equations as well as the position vector for slant-slant helices which a generalization of general helices and slant helices. Also, we present some characterizations theorems for k-slant helices and derived, in gen- eral form, the intrinsic equations for such curves. Thereafter, from a Salkowski curve, anti-salkowski curve, a curve of constant precession and spherical slant helix, as examples of slant helices, we apply this method to nd the paramet- ric representation of some slant-slant helices by means of intrinsic equations. Finally, the parametric representation and the intrinsic equations of Slakowski slant-slant and Anti-Slakowski slant-slant helices have been given.