New special curves and their spherical indicatrices

Abstract

In this paper, we define a new special curve in Euclidean 3-space which we call {\it $k-$slant helix} and introduce some characterizations for this curve. This notation is generalization of a general helix and slant helix. Furthermore, we have given some necessary and sufficient conditions for the $k-$slant helix.

13 pages only

References in corpus (3)

• Curves with constant curvature ratios
• Position vectors of slant helices in Euclidean space E${}^3$
• Determination of the position vectors of general helices from intrinsic equations in $\e^3$

Cited by in corpus (3)

• A New Approach on Curves of Constant Precession
• New Associated Curves k-Principle Direction Curves and N_k Slant Helix
• Spherical Indicatrices of a Bertrand Curve in Three Lie Groups