Spinor Representations of Involute Evolute Curves in E^3

Eri̇şi̇r, Tülay; Kardağ, Neslihan Cansu

doi:10.33401/fujma.562536

Cited by 11 publications

(9 citation statements)

References 11 publications

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“…Let , be the standard inner product of the Euclidean space 3 E , then the following equalities for  …”

Section: Matherials and Methodsmentioning

confidence: 99%

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Involute-Evolute Curves According to Modified Orthogonal Frame

Azak

2021

J. Sci. Arts

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In this paper, the involute-evolute curve concept has been deﬁned according to two type modiﬁed orthogonal frames at non-zero points of curvature and torsion in the Euclidean space E^3 , respectively. Later, the characteristic theorems related to the distance between the corresponding points of these curves have been given. Besides, the relations have been found between the curvatures and also torsions of the two type the involute-evolute modiﬁed orthogonal pairs.

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“…Let , be the standard inner product of the Euclidean space 3 E , then the following equalities for  …”

Section: Matherials and Methodsmentioning

confidence: 99%

“…Thus, the original curve is called an involute curve. In the three dimensional Euclidean space, many studies have been conducted with the involute-evolute curve pair [2][3][4]. Recently, these studies focused on the examination of their characteristic properties according to different frames [5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Involute-Evolute Curves According to Modified Orthogonal Frame

Azak

2021

J. Sci. Arts

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“…in terms of spinors, separately [7]. Now, consider that the curve (β ), which has the same arc-length-parameter s with the curve (α), is a successor curve of the curve (α).…”

Section: Spinor Representation Of Successor Curvesmentioning

confidence: 99%

“…After that, in another study, the spinor formulation of Bishop's frame of curves in three-dimensional Euclidean space was obtained [20]. In addition, Eris ¸ir and Kardaǧ obtained spinor equations of involute-evolute curve pairs in three-dimensional Euclidean space [7]. In another study, spinor formulation of Bertrand curves was given [8].…”

Section: Introductionmentioning

confidence: 99%

Spinor Equations of Successor Curves

Eri̇şi̇r

ÖZTAŞ

2022

Universal Journal of Mathematics and Applications

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The aim of this study is to give spinor representation of successive curves in three-dimensional Euclidean space. In three dimensional Euclidean Space, the spinor representations of a curve with unit speed and a successor curve with the same arc length parameter as this curve has been studied. For this, first of all, the curve with unit speed and its successor curve have been corresponded to two different spinors. Then, using the relationships between these curves, the relationships between the spinors corresponding to these curves have been given. Therefore, geometric interpretations of these curves and corresponding spinors have been made. In addition, different spinor equations of the mates and derivatives of spinors have been examined and geometric interpretations of these spinor equations have been given. Then, spinor equations have been obtained in case the successive curves are helices. Consequently, two examples have been given.

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“…where ε B = B, B L = ±1 and ε T = T, T L = ±1, [5]. Some studies which are studied in the Minkowski 3-dimensional space can be found in [6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Siacci's Theorem for Frenet Curves in Minkowski 3-Space

Özen

2020

Mathematical Sciences and Applications E-Notes

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For motion of a material point along a space curve, due to Siacci [1], a resolution of the acceleration vector is well known. In this resolution, the acceleration vector is stated as the sum of two special oblique components in the osculating plane to the curve. In this paper, we have studied the Siacci's theorem for non-relativistic particles moving along the Frenet curves at very low speeds relative to the speed of light in Minkowski 3-space. Moreover, an illustrative example is given to show how the aforesaid theorem works. This theorem is a new contribution to the field and it may be useful for some specific applications in theoretical, mathematical and computational physics.

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Spinor Representations of Involute Evolute Curves in E^3

Cited by 11 publications

References 11 publications

Involute-Evolute Curves According to Modified Orthogonal Frame

Involute-Evolute Curves According to Modified Orthogonal Frame

Spinor Equations of Successor Curves

Siacci's Theorem for Frenet Curves in Minkowski 3-Space

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