In this work, we use the formal definition of $k$-slant helix cite{ali2} to obtain the intrinsic equations as well as the position vector for emph{slant-slant helices} which a generalization of emph{general helices} and emph{slant 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 emph{slant-slant} helices by means of intrinsic equations. Finally, the parametric representation and the intrinsic equations of textit{Slakowski slant-slant} and textit{Anti-Slakowski slant-slant} helices have been given.
Ali,A T.. (2017). Generalization of general helices and slant helices. Journal of Mahani Mathematical Research, 6(1), 25-41. doi: 10.22103/jmmrc.2017.10467.1042
MLA
Ali,A T.. "Generalization of general helices and slant helices", Journal of Mahani Mathematical Research, 6, 1, 2017, 25-41. doi: 10.22103/jmmrc.2017.10467.1042
HARVARD
Ali A T.. (2017). 'Generalization of general helices and slant helices', Journal of Mahani Mathematical Research, 6(1), pp. 25-41. doi: 10.22103/jmmrc.2017.10467.1042
CHICAGO
A T. Ali, "Generalization of general helices and slant helices," Journal of Mahani Mathematical Research, 6 1 (2017): 25-41, doi: 10.22103/jmmrc.2017.10467.1042
VANCOUVER
Ali A T.. Generalization of general helices and slant helices. J. Mahani Math. Res.. 2017;6(1):25-41. doi: 10.22103/jmmrc.2017.10467.1042
