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

Emel Karaca; Emel Karaca

doi:10.3934/math.20241111

AIMS Mathematics

2024, Volume 9, Issue 8: 22842-22858. doi: 10.3934/math.20241111

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Research article

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

Emel Karaca ^,

Department of Mathematics, Ankara Hacı Bayram Veli University, Ankara, Turkey

Received: 19 April 2024 Revised: 02 July 2024 Accepted: 09 July 2024 Published: 24 July 2024
MSC : 53A25, 53C50, 14J26

A slant ruled surface is a unique type of ruled surface composed by Frenet vectors that form a constant angle with each other and with specific directions in space. In this paper, the non-null slant ruled surface, which is generated by the striction curve of the natural lift curve, was constructed with a novel approximation in $ E^{3}_{1} $. To establish the approximation, E. Study mapping was then applied to determine the relationship between pseudo-spheres and non-null slant ruled surfaces that are generated by the striction curves of the natural lift curves. Furthermore, $ \vec{\bar{q}}-, \vec{\bar{h}}-, \vec{\bar{a}}- $ spacelike (resp., timelike) slant ruled surfaces were classified by using the striction curves of the natural lift curves in $ E^{3}_{1} $. We also provided examples to illustrate the findings.
- tangent bundle of pseudo-sphere,
- non-null vectors,
- slant ruled surface
Citation: Emel Karaca. Non-null slant ruled surfaces and tangent bundle of pseudo-sphere[J]. AIMS Mathematics, 2024, 9(8): 22842-22858. doi: 10.3934/math.20241111

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Abstract

A slant ruled surface is a unique type of ruled surface composed by Frenet vectors that form a constant angle with each other and with specific directions in space. In this paper, the non-null slant ruled surface, which is generated by the striction curve of the natural lift curve, was constructed with a novel approximation in $ E^{3}_{1} $. To establish the approximation, E. Study mapping was then applied to determine the relationship between pseudo-spheres and non-null slant ruled surfaces that are generated by the striction curves of the natural lift curves. Furthermore, $ \vec{\bar{q}}-, \vec{\bar{h}}-, \vec{\bar{a}}- $ spacelike (resp., timelike) slant ruled surfaces were classified by using the striction curves of the natural lift curves in $ E^{3}_{1} $. We also provided examples to illustrate the findings.

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