Untitled

Divjak, Blaženka; Milin-Šipuš, Zcaron

doi:10.1023/a:1022821824927

Cited by 26 publications

(2 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A non-lightlike isotropic vector is a unit vector if u 2 2 − u 2 3 = ±1 [11,12]. See [13][14][15] for more information. The orthogonality of the vectors a = (0, a 2 , a 3 ) and b = (0, b 2 , b 3 ), i.e., a ⊥ b means a b = 0.…”

Section: Preliminaries On Pseudo-galilean Geometrymentioning

confidence: 99%

See 1 more Smart Citation

On admissible curves and their evolution equations in pseudo-Galilean space

Abdel-Aziz¹,

Serry²,

El-Adawy³

et al. 2021

J. Math. Computer Sci.

View full text Add to dashboard Cite

The evolution equations of some forms of admissible curves in the pseudo-Galilean Space G 1 3 are investigated in this paper. In more detail, we use two separate methods to obtain coupled nonlinear partial differential equations of time evolution in terms of their curvatures. The first method studies the evolution equations for admissible curves via the frame field, while the second studies the evolution equations via the velocity vector. Then, the position vectors of the evolving curves are formulated. Also, we conduct comparative research of the evolution equations for curves in different spaces. We furthermore present some models as an application of the evolution equations of the curvature and torsion for admissible curves, confirming our theoretical results.

show abstract

Section: Preliminaries On Pseudo-galilean Geometrymentioning

confidence: 99%

“…Allow Γ : I → G 1 3 , I ⊂ R be an admissible curve parametrized by the pseudo-Galilean invariant parameter s = ζ, as mentioned previously. Then Frenet formulas are as follows [7,12,13]…”

Section: The Admissible Curves Of the First Typementioning

confidence: 99%

On admissible curves and their evolution equations in pseudo-Galilean space

Abdel-Aziz¹,

Serry²,

El-Adawy³

et al. 2021

J. Math. Computer Sci.

View full text Add to dashboard Cite

show abstract

The new characterization of ruled surfaces corresponding dual Bézier curves

İncesu

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

Let be a Bézier curve in D3, that is, the control points of are the vectors in D3 = {u = (u1, u2, u3) : ui ∈ D,i = 1,2,3} which is the set of dual vectors whose each coordinate components are dual numbers defined as a+εa* : a,a* ∈ R,ε ≠ 0; ε2 = 0. So the spherical projection of is a spherical curve denoted by on the unit sphere in D3 and every point of corresponds to a directed line in real space R3 by Study transformation. In this study, the ruled surface X(t, ν) corresponding to this projection curve of dual Bézier curve is stated in terms of the parametric equation of the real and dual part of a given dual Bézier curve . Also, in this study, some fundamental characteristics such as the striction curve, the Gaussian curvature, and the distribution parameter of the ruled surface X(t, ν) corresponding to this projection curve of the dual Bézier curve are investigated. These concepts at any point are stated in terms of the control points of the given dual Bézier curve .

show abstract

The 2‐ruled hypersurfaces in Minkowski 4‐space and their constructions via octonions

Ndiaye,

Özdemir

2023

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we define three types of 2‐ruled hypersurfaces in the Minkowski 4‐space . We obtain Gaussian and mean curvatures of the 2‐ruled hypersurfaces of type‐1 and type‐2 and some characterizations about its minimality. We also deal with the first Laplace–Beltrami operators of these types of 2‐ruled hypersurfaces in . Moreover, the importance of this paper is the definition of these surfaces by using the octonions in . Thus, this is a new idea and makes the paper original. We give an example of 2‐ruled hypersurface constructed by octonion, and we visualize the projections of the images with MAPLE program. Furthermore, the optical fiber can be defined as a one‐dimensional object embedded in the four‐dimensional Minkowski space . Thus, as a discussion, we investigate the geometric evolution of a linearly polarized light wave along an optical fiber by means of the 2‐ruled hypersurfaces in a four‐dimensional Minkowski space.

show abstract

Untitled

Cited by 26 publications

References 2 publications

On admissible curves and their evolution equations in pseudo-Galilean space

On admissible curves and their evolution equations in pseudo-Galilean space

The new characterization of ruled surfaces corresponding dual Bézier curves

The 2‐ruled hypersurfaces in Minkowski 4‐space and their constructions via octonions

Contact Info

Product

Resources

About