Tangential developable surfaces as bonnet surfaces

Roussos, Ioannis M.

doi:10.1007/bf02650670

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…This isometry obviously preserves H = H (s) at the corresponding points. (See Roussos 1988b1999b, Soyuçok 1995. From these three facts we conclude that all helicoidal surfaces are Bonnet surfaces (see Roussos 1988b).…”

Section: G) Further Known Factsmentioning

confidence: 84%

Surfaces in E³ invariant under a one parameter group of isometries of E³

Roussos

2000

An. Acad. Bras. Ciênc.

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We develop a convenient surface theory in E 3 in order to apply it to the class of the surfaces invariant under a one-parameter group of isometries of E 3 . In this way we derive intrinsic characterizations along with several results of subclasses of this class of surfaces that satisfy certain preassigned properties. In the process all results are also effortlessly derived. Among these subclasses are those with surfaces; of constant mean curvature, of constant Gaussian curvature, isothermic, with constant difference or ratio of the principal curvatures.

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Section: G) Further Known Factsmentioning

confidence: 84%

Surfaces in E³ invariant under a one parameter group of isometries of E³

Roussos

2000

An. Acad. Bras. Ciênc.

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“…Characterization for isometric deformation preserving the principal curvatures of surfaces was obtained by the aid of differential forms by Chern in [4]. The geometric characterizations of helicoidal surfaces of constant mean curvature, helicoidal surfaces as Bonnet surfaces, and tangent developable surfaces as Bonnet surfaces were studied by Roussos in [5], [6] and [7], respectively. Roussos obtained a characterization for isometric deformation preserving the mean curvature by using the method of Chern.…”

Section: Introductionmentioning

confidence: 99%

Timelike Tangent Developable Surfaces and Bonnet Surfaces

Ersoy

Eren

2016

Abstract and Applied Analysis

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A criterion was given for a timelike surface to be a Bonnet surface in 3-dimensional Minkowski space by Chen and Li, 1999. In this study, we obtain a necessary and sufficient condition for a timelike tangent developable surface to be a timelike Bonnet surface by the aid of this criterion. This is examined under the condition of the curvature and torsion of the base curve of the timelike developable surface being nonconstant. Moreover, we investigate the nontrivial isometry preserving the mean curvature for a timelike flat helicoidal surface by considering the curvature and torsion of the base curve of the timelike developable surface as being constant.

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“…S. S. Chern asli eğrilikleri koruyan yüzeylerin izometrik deformasyonu için diferansiyel formlar yardımıyla bir karakterizasyon elde etmiştir [4]. Konu ile ilgili pek çok çalışması olan I. M. Roussos, sırasıyla, [5], [6] ve [7]…”

Section: Introductionunclassified

Timelike Bonnet surfaces with non-constant curvature

Ersoy¹,

Eren²

2013

SAUFBE Derg

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Bu çalışmada, 3-boyutlu Minkowski uzayında [11]'de verilen bir timelike yüzeyin Bonnet yüzey olma kriteri göz önüne alındı ve [6]'da I. M. Roussos'un Öklid uzayında yaptığı sınıflandırmaya benzer şekilde Minkowski uzayında Bonnet yüzey olan timelike yüzeyler 1 C , 2 C ve 3 C olmak üzere üç farklı sınıfta incelendi. 1 C de verilen timelike yüzeyler sabit ortalama eğrilikli olup bu durum [11]'de ayrıntılı olarak incelenmiştir. Bu çalışmada ise 2 C ve 3 C durumları incelerek sabit olmayan ortalama eğrilikli timelike yüzeylerin Bonnet yüzey olma kriteri belirlendi.

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Tangential developable surfaces as bonnet surfaces

Cited by 4 publications

References 13 publications

Surfaces in E³ invariant under a one parameter group of isometries of E³

Surfaces in E³ invariant under a one parameter group of isometries of E³

Timelike Tangent Developable Surfaces and Bonnet Surfaces

Timelike Bonnet surfaces with non-constant curvature

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