On Generalized Rotational Surfaces in Euclidean Spaces

Arslan, Kadri; Bulca, Betül; Kosova, Didem

doi:10.4134/jkms.j160330

Cited by 12 publications

(7 citation statements)

References 8 publications

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“…Rotational surfaces in R 4 was first introduced by Moore in 1919 [22]. In the recent years some mathematicians have taken an interest in the rotational surfaces in R 4 ; see for example [7,16,17]. In [17], the authors applied the invariance theory of surfaces in R 4 to the class of general rotational surfaces whose meridians lie in two dimensional planes in order to find all minimal surfaces (see also [15,26] for the rotational surfaces with constant Gaussian curvature in R 4 ).…”

Section: General Rotational ξ−Surfacesmentioning

confidence: 99%

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General rotational ξ−surfaces in Euclidean spaces

Arslan¹,

Aydin²,

Bulca³

2021

Turk J Math

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The general rotational surfaces in the Euclidean 4-space R 4 was first studied by Moore (1919). The Vranceanu surfaces are the special examples of these kind of surfaces. Self-shrinker flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, ξ− surfaces are the generalization of self-shrinker surfaces. In the present article we consider ξ− surfaces in Euclidean spaces. We obtained some results related with rotational surfaces in Euclidean 4− space R 4 to become self-shrinkers. Furthermore, we classify the general rotational ξ− surfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational ξ− surfaces in R 4 .

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Section: General Rotational ξ−Surfacesmentioning

confidence: 99%

“…are the smooth functions on M [7]. With respect to this frame we can obtain the second fundamental maps; where…”

Section: General Rotational ξ−Surfacesmentioning

confidence: 99%

General rotational ξ−surfaces in Euclidean spaces

Arslan¹,

Aydin²,

Bulca³

2021

Turk J Math

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“…Also, the geometry of surfaces such as, rotational surfaces, ruled surfaces, rational Bezier surfaces, rational B-spline surfaces, non-uniform rational B-spline surfaces, discrete surfaces and etc. have been studied by geometers and engineers widely in Euclidean space, Minkowski space, Galilean space, pseudo-Galilean space and etc [1,2,3,4,5,7,8]. For example, E. Octafiatiningsih and I. Sujarwo have used Quadratic Bezier curve on rotational and symmetrical lampshade in [9].…”

Section: Introductionmentioning

confidence: 99%

Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves

2019

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Dönel yüzeylerin şekillerinin ayarlanmasında geometrik tasarımın istenilen şekilde olması için, ilk olarak iki yerel şekil parametreli kübik Hermityan ve kübik Bezier eğrileri kullanılarak dönel yüzeyler oluşturuldu. Oluşturulan bu yeni dönel yüzeylerin, yerel şekil parametrelerinin değiştirilmesi ile yüzeylerin şekillerinin ayarlanması konusunda iyi bir performansa sahip olduğu görüldü. Ayrıca, kübik Hermityan ve kübik Bezier eğrileri tarafından oluşturulan dönel yüzeyler, ilgi çekici yüzeylerin tasarımı için değerli bir yol sağlamaktadır. Bu bağlamda, bu dönel yüzeylerin ortalama ve Gauss eğrilikleri elde edilerek, bu yüzeyler için bazı karakterizasyonlar verildi.

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“…IE 4 Furthermore, in [14], the authors characterized this surface and gave some examples. Also, some surfaces and curves in four dimensinal spaces can be found in [15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%