On tubular surfaces with modified orthogonal frame in Galilean space G3

Kızıltuğ, Sezai; Çakmak, Ali; Eri̇şi̇r, Tülay; Mumcu, Gökhan

doi:10.2298/tsci22s2571k

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2023

2024

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Cited by 2 publications

(1 citation statement)

References 15 publications

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“…As a result, a number of mathematicians came up with frames that can deal with points in Euclidean, Minkowski, and Galilean geometry when the curvature is zero. These frames include the Bishop frame, the modified frame, the equiform frame, and the Darboux frame [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

On Some Quasi-Curves in Galilean Three-Space

Elsharkawy,

Tashkandy,

Emam

et al. 2023

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In this paper, the quasi-frame and quasi-formulas are introduced in Galilean three-space. In addition, the quasi-Bertrand and the quasi-Mannheim curves are studied. It is proven that the angle between the tangents of two quasi-Bertrand or quasi-Mannhiem curves is not constant. Furthermore, the quasi-involute is studied. Moreover, we prove that there is no quasi-evolute curve in Galilean three-space. Also, we introduce quasi-Smarandache curves in Galilean three-space. Finally, we demonstrate an illustrated example to present our findings.

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Section: Introductionmentioning

confidence: 99%

On Some Quasi-Curves in Galilean Three-Space

Elsharkawy,

Tashkandy,

Emam

et al. 2023

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Quasi-position vector curves in Galilean 4-space

Elsharkawy,

Elsharkawy

2024

Front. Phys.

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The Frenet frame is not suitable for describing the behavior of the curve in the Galilean space since it is not defined everywhere. In this study, an alternative frame, the so-called quasi-frame, is investigated in Galilean 4-space. Furthermore, the quasi-formulas in Galilean 4-space are deduced and quasi-curvatures are obtained in terms of the quasi-frame and its derivatives. Quasi-rectifying, quasi-normal, and quasi-osculating curves are studied in Galilean 4-space. We prove that there is no quasi-normal and accordingly normal curve in Galilean 4-space.

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On tubular surfaces with modified orthogonal frame in Galilean space G3

Cited by 2 publications

References 15 publications

On Some Quasi-Curves in Galilean Three-Space

On Some Quasi-Curves in Galilean Three-Space

Quasi-position vector curves in Galilean 4-space

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