An Examination of the Condition Under Which a Conchoidal Surface Is a Bonnet Surface in the Euclidean 3-Space

Aslan, Muradiye Çimdiker; Şekercı, Gülşah Aydin

doi:10.22190/fumi210227047c

Cited by 2 publications

(4 citation statements)

References 11 publications

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“…respectively [13][14][15]. Thus, from (7) the Gauss and mean curvature of the twisted surface X(s, t) in Euclidean 3-space are…”

Section: Methodsmentioning

confidence: 99%

“…respectively, where k(t) = 1, refs. [7][8][9][10][11][12][13]. Let M be a smooth surface in E 3 given with the patch X(s, t) for (s, t) ∈ D ⊂ E 2 .…”

Section: Methodsmentioning

confidence: 99%

“…Dede (2013) computed the types of spacelike conchoid curves in the Minkowski plane [12]. Aslan and Şekerci (2021) examined the condition which is the conchoidal surface and the surface of revolution given with a conchoid curve to be a Bonnet surface in Euclidean 3-space. Additionally, the condition required for the conchoidal surface to be a Bonnet surface is that conchoidal surfaces of constant mean curvature are assumed to be infinitely isothermic Weingarten conchoidal surfaces are investigated in [13].…”

Section: Introductionmentioning

confidence: 99%

“…Aslan and Şekerci (2021) examined the condition which is the conchoidal surface and the surface of revolution given with a conchoid curve to be a Bonnet surface in Euclidean 3-space. Additionally, the condition required for the conchoidal surface to be a Bonnet surface is that conchoidal surfaces of constant mean curvature are assumed to be infinitely isothermic Weingarten conchoidal surfaces are investigated in [13]. Ikawa (2000) found that Bour's theorem revealed the helicoid and the rotational surface with additional conditions having the same Gaussian map on it [14].…”

Section: Introductionmentioning

confidence: 99%

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The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space

2023

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A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature.

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“…respectively [13][14][15]. Thus, from (7) the Gauss and mean curvature of the twisted surface X(s, t) in Euclidean 3-space are…”

Section: Methodsmentioning

confidence: 99%

“…respectively, where k(t) = 1, refs. [7][8][9][10][11][12][13]. Let M be a smooth surface in E 3 given with the patch X(s, t) for (s, t) ∈ D ⊂ E 2 .…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space

2023

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Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$

BULCA SOKUR,

DİRİM

2023

Universal Journal of Mathematics and Applications

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In this paper, we study the conchodial surfaces in 3-dimensional Euclidean space with the condition $\Delta x_{i}=\lambda _{i}x_{i}$ where $\Delta $ denotes the Laplace operator with respect to the first fundamental form. We obtain the classification theorem for these surfaces satisfying under this condition. Furthermore, we have given some special cases for the classification theorem by giving the radius function $r(u,v)$ with respect to the parameters $u$ and $v$.

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An Examination of the Condition Under Which a Conchoidal Surface Is a Bonnet Surface in the Euclidean 3-Space

Cited by 2 publications

References 11 publications

The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space

The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space

Conchoidal Surfaces in Euclidean 3-space Satisfying $\Delta x_{i}=\lambda _{i}x_{i}$

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