On ruled surface in 3-dimensional almost contact metric manifold

Karacan, Murat Kemal; Yüksel, Nural; Ikiz, Hasibe

doi:10.1142/s0219887817500761

Cited by 6 publications

(6 citation statements)

References 4 publications

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“…Substituting (25) into (24) and then considering the constant terms of the equation obtained in such a way, we get…”

Section: Characterization Of Cylinders Over Spatial Base Curvesmentioning

confidence: 99%

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Gauss Map and Its Applications on Ruled Submanifolds in Minkowski Space

Jung¹,

Kim²

2018

Symmetry

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We study ruled submanifolds in Minkowski space in regard to the Gauss map satisfying some partial differential equation. As a generalization of usual cylinders, cones and null scrolls in a three-dimensional Minkowski space, a cylinder over a space curve, a product manifold of a right cone and a k-plane, a product manifold of a hyperbolic cone and a k-plane which look like kinds of cylinders over cones in 3-space, and the generalized B-scroll kind in Minkowski space are characterized with the partial differential equation regarding the Gauss map, where k is a positive integer.

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“…Substituting (25) into (24) and then considering the constant terms of the equation obtained in such a way, we get…”

Section: Characterization Of Cylinders Over Spatial Base Curvesmentioning

confidence: 99%

“…The notion of ruled submanifold is a concept of great interest in the Riemannian geometry, which has been investigated by many authors. Several results involving ruled submanifolds in manifolds equipped with remarkable geometric structures were recently obtained in [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Gauss Map and Its Applications on Ruled Submanifolds in Minkowski Space

Jung¹,

Kim²

2018

Symmetry

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“…In [12], the ruled surface according to the Darboux frame was introduced. In [13], in 3-dimensional contact metric manifold, the properties of the ruled surface were defined. In [14], some geometric interpretations for timelike ruled surfaces were examined.…”

Section: Introductionmentioning

confidence: 99%

An Examination for the Intersection of Two Ruled Surfaces

Karaca

2023

Preprint

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In this study, firstly, each natural lift curve of the main curve is corresponded to the ruled surface by exploitting E. Study mapping and the relation among the subset of the tangent bundle of unit 2-sphere, TM¯ and ruled surfaces in IR3. Secondly, the intersection of two ruled surfaces, which are obtained by using the relation given above, is examined for the condition of the zero-set of λ(u,v)=0. Then, all redundant and non-redundant solutions of the zero-set are investigated. Furthermore, the degenerate situations (u,v)=0, where the whole plane is degenerated by the zero-set,, are denoted. Finally, some examples are given to verify the results. Mathematics Subject Classification (2010). 11B83; 11B37; 05A15.

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“…The ruled surfaces are used in robotics, architecture, mechanics, and other areas. These surfaces are studied in many spaces such as Euclidean, Lorenzian, Galilean, and pseudo‐Galilean spaces 4–8,10,50–64 …”

Section: Introductionmentioning

confidence: 99%

“…These surfaces are studied in many spaces such as Euclidean, Lorenzian, Galilean, and pseudo-Galilean spaces. [4][5][6][7][8]10,[50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] In this paper, the dual Bézier curves have been discussed. When a dual Bézier curve is given, the corresponding dual unit spherical projection curve and its corresponding ruled surface can be discussed.…”

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confidence: 99%

The new characterization of ruled surfaces corresponding dual Bézier curves

İncesu

2021

Math Methods in App Sciences

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Let be a Bézier curve in D3, that is, the control points of are the vectors in D3 = {u = (u1, u2, u3) : ui ∈ D,i = 1,2,3} which is the set of dual vectors whose each coordinate components are dual numbers defined as a+εa* : a,a* ∈ R,ε ≠ 0; ε2 = 0. So the spherical projection of is a spherical curve denoted by on the unit sphere in D3 and every point of corresponds to a directed line in real space R3 by Study transformation. In this study, the ruled surface X(t, ν) corresponding to this projection curve of dual Bézier curve is stated in terms of the parametric equation of the real and dual part of a given dual Bézier curve . Also, in this study, some fundamental characteristics such as the striction curve, the Gaussian curvature, and the distribution parameter of the ruled surface X(t, ν) corresponding to this projection curve of the dual Bézier curve are investigated. These concepts at any point are stated in terms of the control points of the given dual Bézier curve .

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On ruled surface in 3-dimensional almost contact metric manifold

Cited by 6 publications

References 4 publications

Gauss Map and Its Applications on Ruled Submanifolds in Minkowski Space

Gauss Map and Its Applications on Ruled Submanifolds in Minkowski Space

An Examination for the Intersection of Two Ruled Surfaces

The new characterization of ruled surfaces corresponding dual Bézier curves

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