2-Ruled hypersurfaces in Euclidean 4-space

Altin, Mustafa; Kazan, Ahmet; Yoon, Dae Won

doi:10.1016/j.geomphys.2021.104236

Cited by 7 publications

(5 citation statements)

References 8 publications

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“…Altin et al [8] obtain the Gauss map (unit normal vector field) of a 2-ruled hypersurface in Euclidean 4-space with the aid of its general parametric equation. They also obtain Gaussian and mean curvatures of the 2-ruled hypersurface, and they give some characterizations about its minimality.…”

Section: Introductionmentioning

confidence: 99%

The 2‐ruled hypersurfaces in Minkowski 4‐space and their constructions via octonions

Ndiaye,

Özdemir

2023

Math Methods in App Sciences

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In this paper, we define three types of 2‐ruled hypersurfaces in the Minkowski 4‐space . We obtain Gaussian and mean curvatures of the 2‐ruled hypersurfaces of type‐1 and type‐2 and some characterizations about its minimality. We also deal with the first Laplace–Beltrami operators of these types of 2‐ruled hypersurfaces in . Moreover, the importance of this paper is the definition of these surfaces by using the octonions in . Thus, this is a new idea and makes the paper original. We give an example of 2‐ruled hypersurface constructed by octonion, and we visualize the projections of the images with MAPLE program. Furthermore, the optical fiber can be defined as a one‐dimensional object embedded in the four‐dimensional Minkowski space . Thus, as a discussion, we investigate the geometric evolution of a linearly polarized light wave along an optical fiber by means of the 2‐ruled hypersurfaces in a four‐dimensional Minkowski space.

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Section: Introductionmentioning

confidence: 99%

The 2‐ruled hypersurfaces in Minkowski 4‐space and their constructions via octonions

Ndiaye,

Özdemir

2023

Math Methods in App Sciences

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“…In [13], the author gave properties of the slant ruled surfaces in E 3 . In [28], in Euclidean 4-space, some characterizations were examined for 2-ruled surfaces. The term "natural lift curve," which is obtained by the unit tangent vectors of the main curve, was originally used in [22].…”

Section: Introductionmentioning

confidence: 99%

Tangent bundle of pseudo-sphere and Non-null slant ruled surfaces

Karaca

2023

Preprint

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A unique type of ruled surface called a slant ruled surface has some fixed directions in the space and Frenet vectors that form a constant angle with one another. In this study, we construct the novel approximation for this slant ruled surface, also known as a non-null slant ruled surface, which was obtained by the striction curve of the natural lift curve. The relationship between the slant ruled surfaces acquired by the striction curves of the natural lift curves and pseudo-spheres is then derived via E. Study mapping. Furthermore, the striction curves of the natural lift curves in $E^{3}_{1}$ are used to classify as $\vec{\bar{q}}-,\vec{\bar{h}}-,\vec{\bar{a}}-$ spacelike (resp., timelike) slant ruled surfaces. We also provide some additional cases that may illustrate the important results.

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“…The lines of this family are called the generators of the ruled surface. In literature, the properties of these surfaces have been studied in different spaces, [11][12][13][14][15]. Moreover, by using the theorems and definitions of dual space in [16], the isomorphism among unit dual sphere, the tangent bundle of unit 2-sphere, and non-cylindirical ruled surfaces are investigated in [17].…”

Section: Introductionmentioning

confidence: 99%

Singularities of the Ruled Surfaces According to RM Frame and Natural Lift Curves

Karaca

2022

Cumhuriyet Science Journal

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In this study, the ruled surface generated by the natural lift curve in IR^3 is obtained by using the isomorphism between unit dual sphere, DS^2 and the subset of the tangent bundle of unit 2-sphere, T\bar{M}. Then, exploitting E. Study mapping and the isomorphism mentioned below, each natural lift curve on T\bar{M} is corresponded to the ruled surface in IR^3. Moreover, the singularities of this ruled surface are examined according to RM vectors and these ruled surfaces have been classified. Some examples are given to support the main results.

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2-Ruled hypersurfaces in Euclidean 4-space

Cited by 7 publications

References 8 publications

The 2‐ruled hypersurfaces in Minkowski 4‐space and their constructions via octonions

The 2‐ruled hypersurfaces in Minkowski 4‐space and their constructions via octonions

Tangent bundle of pseudo-sphere and Non-null slant ruled surfaces

Singularities of the Ruled Surfaces According to RM Frame and Natural Lift Curves

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