On the fundamental forms of the B-scroll with null directrix and Cartan frame in Minkowskian 3-space

Kilicoglu, Seyda; Hacisalihoğlu, H. Hilmi; Şenyurt, Süleyman

doi:10.12988/ams.2015.53230

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…The fundamental forms of the B-scroll with null directrix and Cartan frame in the Minkowskian three-space is examined in [10]. The properties of the B −scroll are also examined in Euclidean three-space and n-space and in Lorentzian three-space and n-space with time-like directrix curve and null rulings (see [7][8][9]).…”

Section: Ruled Surfacementioning

confidence: 99%

Some Results on Frenet Ruled Surfaces Along the Evolute-Involute Curves, Based on Normal Vector Fields in E3

Kilicoglu¹

2016

GIQ

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In this paper we consider eight special Frenet ruled surfaces along to the involute-evolute curves, α * and α respectively, with curvature k 1 ̸ = 0. First we find the excplit equation of Frenet ruled surfaces along the involute curves in terms of the Frenet apparatus of evolute curve α. Also normal vector fields of these Frenet ruled surfaces have been calculated too. Further we give all results for sixteen positions of Normal vector fields of four Frenet ruled surfaces in terms of Frenet apparatus of evolute curve α. These results also give us the positions of eight special Frenet ruled surfaces along to the involute-evolute curves, based on their normal vectors, in terms of curvatures of evolute curve α. We can give the answer of the questions that in which condition we can produce orthogonal surfaces or surfaces with constant angle. For example Darboux ruled surface and involutive tangent ruled surface of an evolute α have the perpendicular normal vector fields.

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Section: Ruled Surfacementioning

confidence: 99%

Some Results on Frenet Ruled Surfaces Along the Evolute-Involute Curves, Based on Normal Vector Fields in E3

Kilicoglu¹

2016

GIQ

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“…Their properties can be found in, e.g., [6,[13][14][15][16]. In [12], authors state that every nondegenerate null scroll can be reparametrized as a certain type of a null scroll called a B -scroll, defined by Graves [10].…”

Section: Introductionmentioning

confidence: 99%

Null scrolls asB-scrolls in Lorentz–Minkowski 3-space

Šipuš¹,

Gajčić²,

Protrka³

2019

Turk J Math

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Null scrolls, i.e. ruled surfaces whose base curve and rulings are both lightlike (null), are Lorentzian surfaces having no Euclidean counterparts. In this work we present reparametrization of nondegenerate null scroll as a Bscroll, i.e. as a ruled surface whose rulings correspond to the binormal vectors of a base curve. We prove that the curvature of a base curve, which determines the Gaussian and mean curvature of a null scroll, is invariant under such a reparametrization. We also determine a one-parameter family of null curves on null scroll which serve as base curves for this kind of reparametrization.

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On the fundamental forms of the B-scroll with null directrix and Cartan frame in Minkowskian 3-space

Cited by 2 publications

References 8 publications

Some Results on Frenet Ruled Surfaces Along the Evolute-Involute Curves, Based on Normal Vector Fields in E3

Some Results on Frenet Ruled Surfaces Along the Evolute-Involute Curves, Based on Normal Vector Fields in E3

Null scrolls asB-scrolls in Lorentz–Minkowski 3-space

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