Open AccessJournal Article
New Special Curves and Developable Surfaces
TLDR
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.Abstract:
We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves Those notions are generalizations of the notion of cylindrical helices One of the results in this paper gives a classification of special developable surfaces under the condition of the existence of such a special curve as a geodesic As a result, we consider geometric invariants of space curves By using these invariants, we can estimate the order of contact with those special curves for general space curves All arguments in this paper are straight forward and classical However, there have been no papers which have investigated slant helices and conical geodesic curves so far as we knowread more
Citations
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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 Article
Characterizations of slant helices in Euclidean 3-space
TL;DR: 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.
Journal ArticleDOI
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.
Journal ArticleDOI
Slant helices in minkowski space e 3
Ahmad T. Ali,Rafael López +1 more
TL;DR: In this article, a curve = (s) in Minkowski 3-space E 3 and denote by f T;N;Bg the Frenet frame of the curve is considered and it is shown that it is a slant helix if there exists a xed direction U of E 3 such that the function ⟨N(s);U ⟩ is constant.
Journal ArticleDOI
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.
References
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Book
Differential geometry of curves and surfaces
TL;DR: This paper presents a meta-geometry of Surfaces: Isometrics Conformal Maps, which describes how the model derived from the Gauss Map changed over time to reflect the role of curvature in the model construction.
Journal ArticleDOI
Differential Geometry of Curves and Surfaces
TL;DR: Struik as discussed by the authors gave a lecture on Classical Differential Geometry by Prof Dirk J Struik Pp viii + 221 (Cambridge, Mass: Addison-Wesley Press, Inc, 1950) 6 dollars
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Generic properties of helices and Bertrand curves
Shyuichi Izumiya,Nobuko Takeuchi +1 more
TL;DR: In this paper, the authors studied generic properties of cylindrical helices and Bertrand curves as applications of singularity theory for plane curves and spherical curves and showed that these properties can be applied to Bertrand and plane curves.
Special curves and raled surfaces
S. Izumiya,N. Takeuchi +1 more
TL;DR: In this article, the cylindrical helix and Bertrand curve were investigated as curves on ruled surfaces and it was shown that the Bertrand curves are related to the mean curvature of the ruled surfaces.