Surfaces family with common Smarandache asymptotic curve

Atalay, Gülnur Şaffak; Kasap, Emi̇n

doi:10.5269/bspm.v34i1.24392

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…kT +N +B1+B2k , respectively. The problem of constructing a family of surfaces from a given some special Smarandache asymptotic curves in Euclidean 3-space has been analyzed in [14] and surfaces using Smarandache asymptotic curves in Galilean space have been studied in [2].…”

Section: Preliminariesmentioning

confidence: 99%

Hypersurface families with Smarandache curves in Galilean 4-space

Altin¹,

Kazan²,

Karadağ³

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Section: Preliminariesmentioning

confidence: 99%

Hypersurface families with Smarandache curves in Galilean 4-space

Altin¹,

Kazan²,

Karadağ³

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…It was Bayram et al (2012) who followed the same idea and constructed the parametric form of surfaces with a common asymptotic curve [4]. There have been other studies characterizing surfaces on which a given specific curve lies on as geodesic, asymptotic and line of curvature ( [1], [2], [3], [5]). Motivated by these, we present the necessary and sufficient conditions to formulate a family of surfaces having both the involute and evolute curves as of each geodesic, asymptotic and curvature line.…”

Section: Introductionmentioning

confidence: 99%

Family of Surfaces with a Common Special Involute and Evolute Curves

Şenyurt

Ayvacı

Canlı

2022

International Electronic Journal of Geometry

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In this paper, we define the necessary and sufficient conditions for a parametric surface on which both the involute and evolute of any given curve lie to be geodesic, asymptotic and curvature line. Then, the first and second fundamental forms of these surfaces are calculated. By using the Gaussian and mean curvatures, the developability and minimality assumptions are drawn, as well. Moreover we extended the idea to the ruled surfaces. Finally, we provide a set of examples to illustrate the corresponding surfaces.

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Surface Family With A Common Bertrand B-Isoasymptotic Curve

Atalay

Ayvacı²

2021

Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Bu çalışma dört bölümden oluşmaktadır. İlk olarak çalışmanın amacı ve daha önce yapılan çalışmalara yer verildi. İkinci bölümde 3-boyutlu Öklid uzayında temel tanım ve teoremler verilerek, Bertrand-B eğri tanımı ve konu ile ilgili temel tanım ve teoremlere değinildi. Üçüncü kısımda 3-boyutlu Öklid uzayında parametrik denklemi ile verilen yüzey üzerinde eğriliği sıfırdan farklı olan bir eğrinin Bertrand B-çiftinin bu yüzey üzerinde isoasimptotik olması için gerekli ve yeterli şartlar elde edilerek, ortak Bertrand-B isoasimptotikli yüzey aileleri problemi ele alındı. Çalışmayı destekleyen örnekler ise Mapple-12 programı kullanılarak bu bölümde verildi. Dördüncü ve son kısımda ise elde edilen sonuçlar tartışılarak yapılabilecek diğer çalışmalar üzerinde duruldu.

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Surfaces family with common Smarandache asymptotic curve

Cited by 4 publications

References 8 publications

Hypersurface families with Smarandache curves in Galilean 4-space

Hypersurface families with Smarandache curves in Galilean 4-space

Family of Surfaces with a Common Special Involute and Evolute Curves

Surface Family With A Common Bertrand B-Isoasymptotic Curve

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