Open AccessJournal Article
Characterizations of slant helices in Euclidean 3-space
TLDR
In this paper, the relation between a general helix and a slant helix was investigated and some differential equations were obtained for a space curve to be a SLL and its Frenet aparatus.Abstract:
In this paper we investigate the relations between a general helix and a slant helix. Moreover, we obtain some differential equations which they are characterizations for a space curve to be a slant helix. Also, we obtain the slant helix equations and its Frenet aparatus.read more
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A new version of Bishop frame and an application to spherical images
Sueha Yilmaz,Melih Turgut +1 more
TL;DR: In this paper, a new version of Bishop frame using a common vector field as binormal vector field of a regular curve was introduced, which is called Type-2 Bishop Frame.
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Associated curves of a Frenet curve and their applications
Jin Ho Choi,Young Ho Kim +1 more
TL;DR: The notion of the principal (binormal)-direction curve and principal-donor curve of a Frenet curve in E 3 is introduced and the relationship of curvature and torsion of its mates is given.
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Position vector of a time-like slant helix in Minkowski 3-space
TL;DR: In this paper, position vector of a time-like slant helix with respect to standard frame of Minkowski space E31 is studied in terms of Frenet equations.
Journal ArticleDOI
A new approach on curves of constant precession
TL;DR: This paper investigates a curve whose spherical images are spherical slant helices and called it as a C - slant helix, obtaining the axis of the curve and Theorem 3.5 via the alternative moving frame and the Sabban frame, respectively.
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Slant helices in three dimensional Lie groups
TL;DR: It is obtained that slant helices in three dimensional Lie groups with a bi-invariant metric and their involutes, spherical images, are defined and some relations between them are given.
References
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Journal Article
New Special Curves and Developable Surfaces
TL;DR: In this article, the authors define new special curves in Euclidean 3-space which they call slant helices and conical geodesic curves Those notions are generalizations of the notion of cylindrical helices.
Journal ArticleDOI
General helices and a theorem of Lancret
TL;DR: In this article, a theorem of Lancret for general helices in a 3-dimensional real-space-form is presented, which gives a relevant difference between hyperbolic and spherical geometries.
Journal ArticleDOI
On slant helix and its spherical indicatrix
Levent Kula,Yusuf Yayli +1 more
TL;DR: It is obtained that the spherical images are spherical helices and it is shown that a curve of constant precession is a slant helix.
Journal ArticleDOI
Null Helices in Lorentzian Space Forms
TL;DR: In this article, the Cartan frame of a null curve is introduced and the associated curvature functions are called Cartan curvatures of the curve, which generalize the reference of Bonnor for null curves in Minkowski space-time.