Abstract
Abstract Pseudo null curves were studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curve are not considered. In this paper, we study weak AW (k) – type and AW (k) – type pseudo null curve in Minkowski 3-space E 1 3 [E_1^3 . We define helix and slant helix according to Bishop frame in E 1 3 [E_1^3 . Furthermore, the necessary and sufficient conditions for the slant helix and helix in Minkowski 3-space are obtained.
Highlights
The ability to "ride" along a three-dimensional space curve and illustrate the properties of the curve, such as curvature and torsion, would be a great asset to Mathematicians
In 1975, Richard Lawrence Bishop first introduced the parallel frame as a new frame which is well defined even if the curve has vanishing second derivative, the parallel frame came to be called the Bishop frame [8, 9, 10]
In [7], a slant helix in Euclidean 3-space was defined by the property that the principal normal makes a constant angle with a fixed direction
Summary
The ability to "ride" along a three-dimensional space curve and illustrate the properties of the curve, such as curvature and torsion, would be a great asset to Mathematicians. It may be possible to compute information about the shape of sequences of DNA using a curve defined by the Bishop frame. A general helix or a curve of constant slope in Euclidean 3-space E3 is defined in such a way that the tangent makes a constant angle with a fixed direction. In [7], a slant helix in Euclidean 3-space was defined by the property that the principal normal makes a constant angle with a fixed direction. Izumiya and Takeuchi showed that α is a slant helix in E3 if and only if the geodesic curvature of the principal normal of a space curve α is a constant function [15, 17, 19]
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