Investigation of non-lightlike tubular surfaces with Darboux frame in Minkowski 3-space

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 3 to study and explain the geometric characteristics of the harmonic evolute surfaces of tubular surfaces. The characterizations of the harmonic evolute surface’s ϱ and ς parameter curves are evaluated, and then, they are compared. Finally, an example of a tubular surface’s harmonic evolute surface is presented, along with visuals of these surfaces.

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“…Let μðρÞ be an arc-length-parameterized curve in E 3 . Then, the tubular surface via the B-Darboux frame has the parametrization [2,12,13]:…”

Section: Obtaining Tubular Surface Via B-darboux Framementioning

confidence: 99%

“…The Frenet frame is the most well-known frame field, although there are others, such as the Darboux frame. There have been several instances of frame studies of this sort, for example, see [1,2].…”

Section: Introductionmentioning

confidence: 99%

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

Solouma

Al-Dayel

2021

Advances in Mathematical Physics

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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><p>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.</p></abstract>

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Investigation of non-lightlike tubular surfaces with Darboux frame in Minkowski 3-space

Cited by 2 publications

References 5 publications

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

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

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

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Investigation of non-lightlike tubular surfaces with Darboux frame in Minkowski 3-space

Cited by 2 publications

References 5 publications

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

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

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

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

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