Singularities of Non-lightlike Developable Surfaces in Minkowski 3-Space

Nazra, Sahar H.; Abdel-Baky, Rashad A.

doi:10.1007/s00009-022-02252-7

Cited by 8 publications

(10 citation statements)

References 22 publications

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“…Hopefully, these scores will be useful in the field of model-based manufacturing of mechanical products, as well as in geometric modeling. The authors plan to apply this work in diverse spaces and discuss the categorization of singularities as they are pointed out in [26,27].…”

Section: Discussionmentioning

confidence: 99%

Bertrand Offsets of Slant Ruled Surfaces in Euclidean 3-Space

Almoneef,

Abdel-Baky

2024

Symmetry

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In this paper, we investigate and specify the Bertrand offsets of slant ruled and developable surfaces in Euclidean 3-space E3. This is accomplished by utilizing the symmetry of slant curves. As a consequence of this, we present the parameterization of the Bertrand offsets for any slant ruled and developable surfaces. In addition to this, we investigate the monarchies of these ruled surfaces and assign them their own unique classification. Also, we illustrate some examples of slant ruled surfaces.

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Section: Discussionmentioning

confidence: 99%

Bertrand Offsets of Slant Ruled Surfaces in Euclidean 3-Space

Almoneef,

Abdel-Baky

2024

Symmetry

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“…The findings presented in this study have the potential to make significant contributions to the field of spatial locomotion, as well as offer practical applications in the domains of mechanical mathematics and engineering. In our forthcoming research, we intend to explore various applications of the kinematicgeometry of one-parameter hyperbolic spatial locomotion in conjunction with singularity theory, submanifold theory, etc., in [22][23][24][25] in order to derive additional novel findings and properties.…”

Section: Discussionmentioning

confidence: 99%

Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions

Almoneef,

Abdel-Baky

2023

Axioms

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This study utilizes the axodes invariants to derive novel hyperbolic proofs of the Euler–Savary and Disteli formulae. The inflection circle, which is widely recognized, is situated on the hyperbolic dual unit sphere, in accordance with the principles of the kinematic theory of spherical locomotions. Subsequently, a timelike line congruence is defined and its spatial equivalence is thoroughly studied. The formulated assertions degenerate into a quadratic form, which facilitates a comprehensive understanding of the geometric features of the inflection line congruence.

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“…Hopefully, these scores will be useful in the field of differential geometry and to physicists and others exploring general relativity theory. Our future research will investigate how the principal findings presented in this study can be applied to generate fresh outcomes in conjunction with soliton theory, submanifold theory, and other pertinent fields that have been discussed in [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49].…”

Section: Discussionmentioning

confidence: 99%

A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space

Nazra,

Abdel-Baky

2023

Symmetry

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The main outcome of this work is the construction of a surface pencil with a similarity to Bertrand curves in Euclidean 3-space E3. Then, by exploiting the Serret–Frenet frame, we deduce the sufficient and necessary conditions for a surface pencil with Bertrand curves as joint curvature lines. Consequently, the expansion to the ruled surface pencil is also designed. As demonstrations of our essential findings, we illustrate some models to emphasize the process.

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Singularities of Non-lightlike Developable Surfaces in Minkowski 3-Space

Cited by 8 publications

References 22 publications

Bertrand Offsets of Slant Ruled Surfaces in Euclidean 3-Space

Bertrand Offsets of Slant Ruled Surfaces in Euclidean 3-Space

Kinematic Geometry of a Timelike Line Trajectory in Hyperbolic Locomotions

A Surface Pencil with Bertrand Curves as Joint Curvature Lines in Euclidean Three-Space

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