Space-like loxodromes on the canal surfaces in Minkowski 3-space

Sönmez, Nilgün; Babaarslan, Murat

doi:10.2298/fil1814821s

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…Recently, studies in Lorentzian space take an important place in the field of mathematical research that can be seen as part of differential geometry (see [17][18][19][20]) as well as kinematics, robotics, computer graphics, and in most areas of physics. Let us recall some fundamental definitions and properties in Lorentzian space that we use in this paper.…”

Section: Basic Conceptsmentioning

confidence: 99%

Applications of Quaternions in Galilean Spaces

Yüca

Yaylı

2022

J. Sci. Arts

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In this paper, Galilean orthogonal matrices in G^5 and G_1^5 are obtained with the help of unit quaternions. Moreover, Galilean orthogonal matrices in G^4 and G_1^4 are acquired. These matrices produce Galilelan motions in Galilean spaces. We investigate the invariance of the plane where shear motion is acting in Galilean and pseudo-Galilean spaces. Additionally, related examples of matrices that belong to both spaces are provided. With a similar method, dual Galilean orthogonal matrices are obtained by using unit dual quaternions. Finally, we strengthen our work with examples and draw their figures to explore visual representations.

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Section: Basic Conceptsmentioning

confidence: 99%

Applications of Quaternions in Galilean Spaces

Yüca

Yaylı

2022

J. Sci. Arts

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“…Also, loxodromes on a twisted surface, on a canal surface, on a helicoidal surface and on a rotational surface in E 3 have been studied in [2], [3], [8] and [16], respectively. Furthermore, spacelike or timelike loxodromes on different surfaces in Lorentz-Minkowski space have been studied in [5], [6], [9], [21] and etc.…”

Section: General Information and Basic Conceptsmentioning

confidence: 99%

Loxodromes on Twisted Surfaces in Lorentz-Minkowski 3-Space

Kazan¹,

Altin²

2021

Preprint

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In the present paper, firstly we give the general formulas according to first fundamental form of a surface for different types of loxodromes, meridians and surfaces in E 3 1 . After that, we obtain the differential equations of loxodromes on Type-I, Type-II and Type-III twisted surfaces in E 3 1 and also, we state a theorem which generalizes the differential equations of different types of loxodromes on the twisted surfaces for a special case. Finally, we provide several examples for visualizing our obtained results and draw our loxodromes and meridians on twisted surfaces with the aid of Mathematica.

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Loxodromes on twisted surfaces in Lorentz–Minkowski 3-space

Kazan

Altin

2022

Asian-European J. Math.

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In this paper, first, we give the general formulas according to first fundamental form of a surface for different types of loxodromes, meridians and surfaces in [Formula: see text]. After that, we obtain the differential equations of loxodromes on Type-I, Type-II and Type-III twisted surfaces in [Formula: see text] and also, we state a theorem which generalizes the differential equations of different types of loxodromes on the twisted surfaces for a special case. Finally, we provide several examples for visualizing our obtained results and draw our loxodromes and meridians on twisted surfaces with the aid of Mathematica.

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Space-like loxodromes on the canal surfaces in Minkowski 3-space

Abstract: In this paper, we obtain the differential equations of the space-like loxodromes on the non-degenerate canal surfaces depending on the causal characters of these canal surfaces and their meridians in Minkowski 3-space. Also we give an example by using Mathematica computer programme.

Cited by 4 publications

References 9 publications

Applications of Quaternions in Galilean Spaces

Applications of Quaternions in Galilean Spaces

Loxodromes on Twisted Surfaces in Lorentz-Minkowski 3-Space

Loxodromes on twisted surfaces in Lorentz–Minkowski 3-space

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