Generalization of general helices and slant helices - Ahmet Ali (Journal of Mahani Mathematical Research, 2017)
In this work, we use the formal definition of $k$-slant helix citeali2 to obtain the intrinsic equations as well as the position vector for emphslant-slant helices which a generalization of emphgeneral helices and emphslant helices. Also, we present some characterizations theorems for $k$-slant helices and derived, in general 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 find the parametric representation of some emphslant-slant helices by means of intrinsic equations. Finally, the parametric representation and the intrinsic equations of textitSlakowski slant-slant and textitAnti-Slakowski slant-slant helices have been given.