The Frenet and Darboux Instantaneous Rotation Vectors of Curves on Time-Like Surface

Uğurlu, H. Hüseyin; Kocayiğit, Hüseyin

doi:10.3390/mca1020133

Cited by 10 publications

(6 citation statements)

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“…If S is a spacelike surface then T × Q = n, Q × n = −T, n × T = −Q. Similarly if S is a timelike surface then T × Q = −n, Q × n = ±T, n × T = ∓Q [2].…”

Section: Definitionmentioning

confidence: 99%

Intrinsic equations for a relaxed elastic line of second kind in Minkowski 3-space

Bayram

Kasap

2015

Filomat

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Let α be an arc on a connected oriented surface S in Minkowski 3space, parameterized by arc length s, with torsion τ and length l. The total square torsion H of α is defined by H = l 0 τ 2 ds. The arc is called a relaxed elastic line of second kind if it is an extremal for the variational problem of minimizing the value of H within the family of all arcs of length l on S having the same initial point and initial direction as α. In this study, we obtain differential equation and boundary conditions for a relaxed elastic line of second kind on an oriented surface in Minkowski 3-space.

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“…If S is a spacelike surface then T × Q = n, Q × n = −T, n × T = −Q. Similarly if S is a timelike surface then T × Q = −n, Q × n = ±T, n × T = ∓Q [2].…”

Section: Definitionmentioning

confidence: 99%

Intrinsic equations for a relaxed elastic line of second kind in Minkowski 3-space

Bayram

Kasap

2015

Filomat

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“…Moreover, s is the arc-length parameter of γ. In particular, the following equations are presented: [17]. Moreover, it is found as the following…”

Section: Fundamental Backgroundsmentioning

confidence: 99%

Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds

Şahin

Özdemi̇r

2022

Hacettepe Journal of Mathematics and Statistics

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In this article, Darboux frame variations for timelike surfaces in semi-Riemannian manifolds are discussed. In addition, the Killing equations are examined by using the Darboux frame curvature variations. Then, magnetic trajectories are generated by means of the variational vector fields. Furthermore, parametric representations of all magnetic trajectories on the de Sitter space S 2 1 are presented. Moreover, various examples of magnetic trajectories are given in order to illustrate the theoretical results.

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“…In this formulae and are called the geodesic curvature, the normal curvature and the geodesic torsion, respectively (Uğurlu and Kocayigit, 1996). The relations between geodesic curvature, the normal curvature, the geodesic torsion and are given as follows:…”

Section: Letmentioning

confidence: 99%

Timelike tubes with Darboux frame in Minkowski 3-space

Kzltu¹,

Yayl²

2013

Int. J. Phys. Sci.

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In this study, we define a timelike tube around a spacelike curve with timelike binormal by taking Darboux frame instead of Frenet frame in Minkowski 3-space. Subsequently, we compute the Gaussian curvature, the mean curvature, and the second Gaussian curvature of timelike tube with Darboux frame and obtained some characterizations for special curves on this timelike tube around a spacelike curve with timelike binormal.

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The Frenet and Darboux Instantaneous Rotation Vectors of Curves on Time-Like Surface

Cited by 10 publications

References 0 publications

Intrinsic equations for a relaxed elastic line of second kind in Minkowski 3-space

Intrinsic equations for a relaxed elastic line of second kind in Minkowski 3-space

Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds

Timelike tubes with Darboux frame in Minkowski 3-space

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