An alternative moving frame for a tubular surface around a spacelike curve with a spacelike normal in Minkowski 3-space

Karacan, Murat Kemal; Bükcü, Bahaddin

doi:10.1007/s12215-008-0013-8

Cited by 12 publications

(9 citation statements)

References 1 publication

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“…Moreover, canal surface is an important instrument in surface modelling for CAD/CAM such as tubular surfaces, torus and Dupin cyclides. If we choose the radius function r(t) as constant, we obtain tubular surfaces [4].…”

Section: A Uçum and Ki̇larslanmentioning

confidence: 99%

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New Types of Canal Surfaces in Minkowski 3-Space

Uçum

İlarslan

2015

Adv. Appl. Clifford Algebras

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Canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve. In Minkowski 3-space, many authors studied canal surfaces. However, when one investigates the papers, it is obvious that the parametrizations of the canal surfaces were found with respect to only pseudo sphere S 2 1 (r). In this paper, we reconsider the canal surfaces for all Lorentz spheres which are pseudo sphere S 2 1 (r), pseudo-hyperbolic sphere H 2 (r) or lightlike cone C and we find the parametrizations of the surfaces. Moreover, we found the parametrization of the tubular surfaces with respect to all Lorentz spheres. Also, we study Weingarten and linear Weingarten type spacelike tubular surface obtained from pseudo-hyperbolic sphere H 2 0 (r) and the singular points of the spacelike tubular surface obtained from pseudo-hyperbolic sphere H 2 0 (r). Mathematics Subject Classification. 53B30, 53C50, 53A35.

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Section: A Uçum and Ki̇larslanmentioning

confidence: 99%

“…Karacan et al [2][3][4][5] consider the canal surfaces and tubular surfaces in Euclidean 3-space, Minkowski 3-space, Galilean and Pseudo Galilean spaces. However, in these article, the spheres used in canal surface are spacelike (that is, only pseudo sphere is used).…”

Section: A Uçum and Ki̇larslanmentioning

confidence: 99%

New Types of Canal Surfaces in Minkowski 3-Space

Uçum

İlarslan

2015

Adv. Appl. Clifford Algebras

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“…Nowadays a good deal of research has been done on Bishop frame in Euclidean space see [4], [5]; in Minkowski space, see [3], [22]; and in dual space, see [14]. And, recently, this special frame is extended to study of canal and tubular surfaces, we refer [12], [13].…”

Section: Troductiomentioning

confidence: 99%

“…In this work we also investigate vector differential equations derived from type-2 Bishop vector fields. ∈ ∈ ∈ ∈ ∈     (13) …”

Section: Vector Differe Tial Equatio Of Third Order Characterizes Regmentioning

confidence: 99%

Classical Differential Geometry of Curves According to Type-2 Bishop Trihedra

Özyilmaz

2011

MCA

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Abstract-In this work, we study classical differential geometry of the curves according to type-2 Bishop trihedra. First, we present some characterizations of a general helix, a helix, special cases and spherical curves. Thereafter, we investigate position vector of a regular curve by a system of ordinary differential equations whose solution gives the components of the position vector with respect to type-2 Bishop frame. Next we prove that the first vector field of the type-2 Bishop frame of a regular curve satisfies a vector differential equation of third order. Solutions of the mentioned system and vector differential equation have not been found. Therefore we present some special characterizations introducing special planes of three dimensional Euclidean space.

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“…For example, it may be possible to compute information about the shope of sequences of DNA using a curve defined by the Bishop frame. The Bishop frame may also provide a new way to control virtual cameras in computer animatons, [21].…”

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confidence: 99%

Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space

Atalay

Kasap

2016

bspm

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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.

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An alternative moving frame for a tubular surface around a spacelike curve with a spacelike normal in Minkowski 3-space

Cited by 12 publications

References 1 publication

New Types of Canal Surfaces in Minkowski 3-Space

New Types of Canal Surfaces in Minkowski 3-Space

Classical Differential Geometry of Curves According to Type-2 Bishop Trihedra

Surfaces family with common smarandache asymptotic curve according to bishop frame in euclidean 3-space

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