Generalization of general helices and slant helices
Publish place: Journal of Mahani Mathematical Research، Vol: 6، Issue: 1
Publish Year: 1396
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_KJMMRC-6-1_003
تاریخ نمایه سازی: 5 خرداد 1398
Abstract:
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.
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Authors
Ahmet Ali
Al-Azhar University
SUHA YILMAZ
BUCA FACULTY OF EDUCATION, DOKUZ EYLUL UNIVERSITY, ۳۵۱۵۰, BUCA-IZMIR, TURKEY,
MURADIYE CIMDIKER
DEPARTMENTS OF MATHEMATICS, KIRKLARELI UNIVERSITY, ۳۹۱۰۰ KIRKLARELI, TURKEY,