Tangent bundle of unit 2-sphere and slant ruled surfaces

Karaca, Emel; Çalışkan, Mustafa

doi:10.2298/fil2302491k

Cited by 4 publications

(1 citation statement)

References 13 publications

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“…In [12], the authors investigated substantial results for the ruled surface in E 3 1 , which is generated by the natural lift curve. In the light of these studies, in [11], the authors found that the natural lift curve on T M is corresponded to a unique ruled surface in E 3 . This study's main goal is to provide a new definition for non-null slant ruled surfaces in E 3 1 .…”

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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Section: Introductionmentioning

confidence: 99%

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

Karaca

2023

Preprint

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Generalized null Cartan helices and principal normal worldsheets in Minkowski 3-space

Xu,

Pei

2024

Mod. Phys. Lett. A

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On preserved properties for slant ruled surfaces under homothety in $E^{3}$

Karaca

2024

Malaya J. Mat.

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In mathematics, it is known that if $E^{3} \rightarrow E^{3}$ is a homothety and $N$ is a surface in $E^{3}$, then $f(N)=\bar{N}$ is a surface in $E^{3}$. In this study, especially, the surface $N$ is considered a slant ruled surface. Then, it is proved that the image surface $f(N)=\bar{N}$ is a slant ruled surface, too. Moreover, some significant properties are shown to be preserved under homothety in $E^{3}$.

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Tangent bundle of unit 2-sphere and slant ruled surfaces

Cited by 4 publications

References 13 publications

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

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

Generalized null Cartan helices and principal normal worldsheets in Minkowski 3-space

On preserved properties for slant ruled surfaces under homothety in \(E^{3}\)

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