Position vectors of a timelike and a null helix in Minkowski 3-space

İlarslan, Kazım; Boyacioglu, Ozguer

doi:10.1016/j.chaos.2008.04.003

Cited by 38 publications

(32 citation statements)

References 12 publications

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“…For instance, see [7], [10], [19], [20] and [23]. In this work, we also study position vector of a regular curve according to type-2 Bishop frame.…”

Section: Positio Vector Of a Regular Curve Accordđ G To Type-2mentioning

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 instance, see [7], [10], [19], [20] and [23]. In this work, we also study position vector of a regular curve according to type-2 Bishop frame.…”

Section: Positio Vector Of a Regular Curve Accordđ G To Type-2mentioning

confidence: 99%

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

Özyilmaz

2011

MCA

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“…Some of these special curves are spacelike curves, timelike curves and null curves. Spacelike curves and timelike curves were initially investigated and developed by several authors [1,2,3,6]. Later, this topic drew attention of several authors and they studied different kinds of curves in the Lorentzian manifolds R 3 1 and R 4 1 .…”

Section: Introductionmentioning

confidence: 99%

“…Ilarslan and O. Boyacioglu studied position vectors of a timelike and a null helice in R 3 1 [6]. K. Ilarslan and E. Nesovic gave some characterizations for null curves in E 4 and they obtained some relations between null normal curves and null osculating curves as well as between null rectifying curves and null osculating curves [10].…”

Section: Introductionmentioning

confidence: 99%

Some characterizations of a timelike curve in $R^3_1$

Sivridag¹,

Akgun²

2016

ntmsci

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“…We know that de Sitter 3-space is a vacuum solution of the Einstein equation and an important cosmological model for physical universe [1,4,6,10,11]. Authors have given the geometrical properties of spacelike or timelike curves in Minkowski space [6,8,12]; B. Mustafa obtained the geometrical properties of involutes of spacelike curves in Minkowski 3-space [9]. However, most of papers and books studying the geometrical properties of general surfaces generated by spacelike curves in Minkowski 4-space nor their hypersurfaces.…”

Section: Introductionmentioning

confidence: 99%