On the Involutive B-Scrolls in the Euclidean Three-Space

Kilicoglu, Seyda

doi:10.7546/giq-13-2012-205-214

Cited by 3 publications

(3 citation statements)

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“…is the parametrization of the ruled surface which is called involutive B-scroll (binormal scroll) of the curve α [11]. The directrix of this surface is the involute curve…”

Section: Ruled Surfacementioning

confidence: 99%

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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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“…is the parametrization of the ruled surface which is called involutive B-scroll (binormal scroll) of the curve α [11]. The directrix of this surface is the involute curve…”

Section: Ruled Surfacementioning

confidence: 99%

“…By using the similiar method we produce a new ruled surface based on the other ruled surface. The Involutive B scrolls are defined in [11]. D scroll, which is known as the rectifying developable surface, of any curve α and the involute D scroll of the curve α are already defined, in Euclidean three-space.…”

Section: Introductionmentioning

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 [6] there are applications of ruled surface.The properties of the B−scroll are also examined in Euclidean 3−space and n−space and in Lorentzian 3−space and n−space with time-like directrix curve and null rulings ( see [10], [11]). Also involutive B − scroll (binormal scroll) of the curve α is defined as in the following definition and examined in [12]. Also ruled surface with Bishop Frame is studied in [13].…”

Section: Introductionmentioning

confidence: 99%

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

Kilicoglu¹,

Hacisalihoğlu²,

Şenyurt³

2015

ams

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In this work we will study on Minkowskian 3−space, with null directrix and Cartan frame.In this paper, we investigate the first fundamental form, the second fundamental form of B-scroll with Cartan framed null directrix in the Minkowskian 3-space. The third fundamental form of Bscroll with Cartan framed null directrix are examined in Minkowskian 3-space. Also we have that the ruled surface B − scroll is minimal surface under the condition −k 1 − uk 2 + u 2 k 3 2 = 0.Mathematics Subject Classification: 53A05, 53A35

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On the Differential Geometric Elements of the Involute $${\tilde{\rm D}}$$ D ~ -Scroll in E 3

Şenyurt

Kilicoglu²

2015

Adv. Appl. Clifford Algebras

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On the Involutive B-Scrolls in the Euclidean Three-Space

Cited by 3 publications

References 0 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

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

On the Differential Geometric Elements of the Involute $${\tilde{\rm D}}$$ D ~ -Scroll in E 3

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