Harmonic Evolute Surface of Tubular Surfaces via <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1">
 <mi mathvariant="double-struck">B</mi>
 </math>-Darboux Frame in Euclidean 3-Space

Solouma, E. M.; Al-Dayel, İbrahim

doi:10.1155/2021/5269655

Advances in Mathematical Physics

2021

DOI: 10.1155/2021/5269655

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Harmonic Evolute Surface of Tubular Surfaces via $B$ -Darboux Frame in Euclidean 3-Space

E. M. Solouma

İbrahim Al-Dayel

Abstract: In this article, we look at a surface associated with real-valued functions. The surface is known as a harmonic surface, and its unit normal vector and mean curvature have been used to characterize it. We use the Bishop-Darboux frame ( B -Darboux frame) in Euclidean 3-space E … Show more

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2024

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Cited by 3 publications

References 10 publications

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On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

Al-Dayel

Solouma

Khan

2022

MATH

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<abstract>In Euclidean 3-space $ {\mathrm{E}}^3 $, a canonical subject is the focal surface of such a cliched space curve, which would be a two-dimensional corrosive with Lagrangian discontinuities. The tubular surfaces with respect to the B-Darboux frame and type-2 Bishop frame in $ {\mathrm{E}}^3 $ are given. These tubular surfaces' focal surfaces are then defined. For such types of surfaces, we acquire some results becoming Weingarten, flat, linear Weingarten conditions and we demonstrate that in $ {\mathrm{E}}^3 $, a tubular surface has no minimal focal surface. We also provide some examples of these types of surfaces.</abstract>

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On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

Al-Dayel

Solouma

Khan

2022

MATH

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Family of ruled surfaces generated by equiform Bishop spherical image in Minkowski 3-space

Solouma

Abdelkawy

2023

MATH

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<abstract>The study of a family of equiform Bishop spherical image ruled surfaces created by some specific curves such as spherical image in Minkowski 3-space using equiform Bishop frame of that curve is presented in this paper. We also offer the necessary criteria for these surfaces to be equiform Bishop developable and equiform Bishop minimum in relation to equiform Bishop curvatures, as well as when the curve is enclosed in a plane. Finally, we provide an example, such as these surfaces.</abstract>

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Characterization of imbricate-ruled surfaces via rotation-minimizing Darboux frame in Minkowski 3-space $ \mathrm{E}_1^3 $

Solouma,

Al-Dayel,

Khan

et al. 2024

MATH

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<abstract>Using a common tangent vector field to a surface along a curve, in this study we discussed a new Darboux frame that we referred to as the rotation-minimizing Darboux frame (RMDF) in Minkowski 3-space. The parametric equation resulting from the RMDF frame for an imbricate-ruled surface was then provided. As a result, minimal (or maximal for timelike surfaces) ruled surfaces were derived, along with the necessary and sufficient criteria for imbricate-ruled surfaces to be developable. The surfaces also described the parameter curves of these surfaces' asymptotic, geodesic, and curvature lines. We also gave an example to emphasize the most significant results.</abstract>

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Harmonic Evolute Surface of Tubular Surfaces via $B$ -Darboux Frame in Euclidean 3-Space

Abstract: In this article, we look at a surface associated with real-valued functions. The surface is known as a harmonic surface, and its unit normal vector and mean curvature have been used to characterize it. We use the Bishop-Darboux frame ( B -Darboux frame) in Euclidean 3-space E … Show more

Cited by 3 publications

References 10 publications

On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

Family of ruled surfaces generated by equiform Bishop spherical image in Minkowski 3-space

Characterization of imbricate-ruled surfaces via rotation-minimizing Darboux frame in Minkowski 3-space $ \mathrm{E}_1^3 $

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Harmonic Evolute Surface of Tubular Surfaces via B -Darboux Frame in Euclidean 3-Space

Cited by 3 publications

References 10 publications

On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space

Family of ruled surfaces generated by equiform Bishop spherical image in Minkowski 3-space

Characterization of imbricate-ruled surfaces via rotation-minimizing Darboux frame in Minkowski 3-space $ \mathrm{E}_1^3 $

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Product

Resources

About

Harmonic Evolute Surface of Tubular Surfaces via $B$ -Darboux Frame in Euclidean 3-Space