On Fibonacci spinors

Eri̇şi̇r, Tülay; Güngör, Mehmet Ali̇

doi:10.1142/s0219887820500656

Cited by 8 publications

(13 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Terefore, many studies for hyperbolic spinors were obtained [30][31][32]. In addition to these studies, Eris ¸ir and Güngör defned Fibonacci spinors, which are spinor representations of Fibonacci and Lucas quaternion sequences [33]. In addition, spinor expressions of Pell and Pell-Lucas quaternions were given in [34].…”

Section: Introductionmentioning

confidence: 99%

Horadam Spinors

Erişir

2024

Journal of Mathematics

View full text Add to dashboard Cite

Spinors can be expressed as Lie algebra of infinitesimal rotations. Spinors are also defined as elements of a vector space which carries a linear representation of the Clifford algebra typically. The motivation for this study is to define a new and particular sequence. An essential feature of this sequence is that while a generalization is being made, spinors, which have a lot of use in physics, are used. This new sequence defined using spinor representations is called the Horadam spinor sequence; formulas such as the Binet formula, generating function formula, and Cassini formula are given. The Horadam spinors given in this study are a generalization of the spinor representations of Horadam quaternion sequences.

show abstract

Section: Introductionmentioning

confidence: 99%

Horadam Spinors

Erişir

2024

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…Spinors are considered as multi linear transformations and by this property, spinors are mathematical structure. According to the mathematicians spinors are a vectorial structure and this multi-linear property does not matter [11,13,14]. The first mathematician who studied the spinors in geometrical sense is Élie Cartan [3].…”

Section: Introductionmentioning

confidence: 99%

“…Cartan stated that these vectors are complex as two-dimensional in the space C 2 . Moreover, Cartan [3] expressed the spinors comprising of two complex components in terms of vectors in Euclidean 3-space and specified that spinors supply a linear representation of the groups of rotations of a space of any dimension [11,13]. The triads of unit vectors which are orthogonal to each other were stated in terms of a single vector having two complex components, that is called a spinor [3,9,10].…”

Section: Introductionmentioning

confidence: 99%

“…The other study with respect to the spinors in geometric meaning is performed by Vivarelli [40]. Afterwards, Vivarelli obtained some relations between the spinors and quaternions, and provided the spinor representation of rotations in E 3 by utilizing the relations between the rotations in E 3 and quaternions [13,40]. In addition to these, hyperbolic spinors were studied [1,12,23,24] in Minkowski 3-space.…”

Section: Introductionmentioning

confidence: 99%

“…Also, spinors have an substantial and basic role in Clifford algebra, which is called geometric algebra by W. K. Clifford, as well [5,27,28,39]. Furthermore, the Fibonacci spinors were investigated in [13].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spinor Representations of Positional Adapted Frame in the Euclidean 3-Space

İşbilir

Özen

Güner

2023

International Electronic Journal of Geometry

View full text Add to dashboard Cite

The main goal of this study is to bring together the spinors, which have a major place in several disciplines from mathematics to physics, and Positional Adapted Frame (PAF) which is a new type frame that attracts the attention of many researchers. In accordance with this purpose, we introduce the spinor representations for the trajectories endowed with PAF in the Euclidean 3-space $\mathbb{E}^3$, and construct the spinor equations of PAF vectors. Then, we find the relations between spinor representations of PAF and Serret-Frenet frame. Also we give some results and present some geometric interpretations with respect to this relationship. Moreover, we present an illustrative numerical example in order to support the given theorems and results.

show abstract

On the quaternionic osculating direction curves

Kızıltuğ

Eri̇şi̇r

Mumcu

2022

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

Quaternions are widely used in physics. Quaternions, an extension of complex numbers, are closely related to many fundamental concepts (e.g. Pauli matrices) in physics. The aim of this study is the geometric structure underlying the quaternions used in physics. In this paper, we have investigated a new structure of unit speed associated curves such as spatial quaternionic and quaternionic osculating direction curves. For this, we have assumed that the vector fields [Formula: see text] where [Formula: see text] for the spatial quaternionic curve [Formula: see text] and [Formula: see text] where [Formula: see text] for the quaternionic curve [Formula: see text]. Then, we have given the relationship between (spatial) quaternionic (OD)-curves and Mannheim curve pair. Moreover, we have examined in which cases the (spatial) quaternionic (OD)-curve can be helix or slant helix. So, considering that helices also take place in electron physics, it is thought that this study will create a bridge between physics and geometry. Finally, we have given the examples and draw the figures of curves in the examples.

show abstract

On Fibonacci spinors

Cited by 8 publications

References 13 publications

Horadam Spinors

Horadam Spinors

Spinor Representations of Positional Adapted Frame in the Euclidean 3-Space

On the quaternionic osculating direction curves

Contact Info

Product

Resources

About