Surfaces family with common null asymptotic (original) (raw)
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Surfaces With A Common Asymptotic Curve According To Bishop Frame In Euclidean 3-Space
arXiv (Cornell University), 2014
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface interpolating a given curve as the asymptotic curve of it. Also, we analyze the conditions when the resulting surface is a ruled surface. Furthermore, we prove that there exists no developable surface possessing a given curve as an asymptotic curve except plane. Finally, we illustrate this method by presenting some examples.
Surface Family with a Common Asymptotic Curve in Minkowski 3-SPACE
2018
In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also present some interesting examples to show the validity of this study. AMS: 53C40, 53C50.
Boletim da Sociedade Paranaense de Matemática, 2016
In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Bishop frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache asymptotic curve.
Surfaces with a common asymptotic curve in Minkowski 3-space
In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also present some interesting examples to show the validity of this study.
Construction of Offset Surfaces with a Given Non-Null Asymptotic Curve
2021
In the present work, we study construction of offset surfaces with a givennon-null asymptotic curve. Let alphaleft(sright)\alpha \left( s\right) alphaleft(sright) be a spacelike ortimelike unit speed curve with non-vanishing curvature and varphileft(s,tright)\varphi \left(s,t\right) varphileft(s,tright) be a surface pencil accepting alphaleft(sright)\alpha \left( s\right) alphaleft(sright) as acommon asymptotic curve. We obtain conditions such that the offset surfacepossesses the image of alphaleft(sright)\alpha \left( s\right) alphaleft(sright) as an asymptotic curve. Wevalidate the method with illustrative examples
Surfaces family with common Smarandache asymptotic curve
Boletim da Sociedade Paranaense de Matemática, 2016
In this paper, we analyzed the problem of constructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficients to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.
Surface Family with a Common Natural Asymptotic Lift of a Timelike Curve in Minkowski 3-space
Celal Bayar Üniversitesi Fen Bilimleri Dergisi
In the present paper, we find a surface family possessing the natural lift of a given timelike curve as a asymptotic in Minkowski 3-space. We express necessary and sufficient conditions for the given curve such that its natural lift is a asymptotic on any member of the surface family. Finally, we illustrate the method with some examples.
International electronic journal of geometry, 2022
In this paper we define the necessary and sufficient conditions for both the involute and evolute of a given curve to be geodesic, asymptotic and curvature line on a parametric surface. 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.