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. (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
Ahmet 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
HARVARD
Ali, A. (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
VANCOUVER
Ali, A. Generalization of general helices and slant helices. Journal of Mahani Mathematical Research, 2017; 6(1): 25-41. doi: 10.22103/jmmrc.2017.10467.1042
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