scholarly journals Integral equations of biharmonic constant π₁-slope curves according to type-2 Bishop frame in the SOL space

2013 ◽  
Vol 31 (2) ◽  
pp. 205 ◽  
Author(s):  
Talat Körpinar ◽  
Essin Turhan
Keyword(s):  
Integral Equations ◽  
Bishop Frame ◽  
Sol Space

In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.

scholarly journals b-Smarandache tm₂ curves of biharmonic new type b-slant helices according to Bishop frame in the Sol space Sol³

2013 ◽  
Vol 31 (2) ◽  
pp. 265
Author(s):  
Talat Körpinar ◽  
Essin Turhan
Keyword(s):  
Type B ◽  
Bishop Frame ◽  
Slant Helix ◽  
New Type ◽  
Sol Space

In this paper, we study b-Smarandache tm₂ curves of biharmonic new type b-slant helix in the Sol³. We characterize the b-Smarandache tm₂ curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Sol³.

Relation between Darboux and type-2 Bishop frames in Euclidean space

2016 ◽  
Vol 13 (07) ◽  
pp. 1650101 ◽  
Author(s):  
Amine Yilmaz ◽  
Emin Özyilmaz
Keyword(s):  
Euclidean Space ◽  
Transition Matrix ◽  
Geodesic Curvature ◽  
Spherical Image ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Spherical Images

In this work, we investigate relationships between Darboux and type-2 Bishop frames in Euclidean space. Then, we obtain the geodesic curvature of the spherical image curve of the Darboux vector of the type-2 Bishop frame. Also, we give transition matrix between the Darboux and type-2 Bishop frames of the type-2 Bishop frames of the spherical images of the edges [Formula: see text] and [Formula: see text]. Finally, we express some interesting relations and illustrate of the examples by the aid Maple programe.

The ruled surfaces according to type-2 Bishop frame in E^3

2017 ◽  
Vol 12 ◽  
pp. 133-143
Author(s):  
Esra Damar ◽  
Nural Yuksel ◽  
Aysel Turgut Vanli
Keyword(s):  
Ruled Surfaces ◽  
Bishop Frame

scholarly journals NEW VERSION OF FERMI-WALKER DERIVATIVES ACCORDING TO THE TYPE-2 BISHOP FRAME WITH ENERGY

2021 ◽  
Vol 21 (1) ◽  
pp. 113-124
Author(s):  
TALAT KORPINAR ◽  
HATICE OZDEMIR ◽  
ZELIHA KORPINAR
Keyword(s):  
Vector Fields ◽  
Bishop Frame ◽  
Energy Relations ◽  
Derivatives Of

In this paper, we obtain the Fermi-Walker derivatives of , , magnetic curves according to the type-2 Bishop frame in the space. Moreover, we obtain the energy of the Fermi-Walker derivative of magnetic curves according to the type-2 Bishop frame in space. Finally, we have energy relations of some vector fields associated with type-2 Bishop frame in the space.

scholarly journals Characteristic Properties of Type-2 Smarandache Ruled Surfaces According to the Type-2 Bishop Frame in E 3

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ibrahim Al-Dayel ◽  
E. M. Solouma
Keyword(s):  
Sufficient Conditions ◽  
Special Kind ◽  
Necessary And Sufficient Conditions ◽  
Ruled Surfaces ◽  
Minimal Amount ◽  
Bishop Frame ◽  
Necessary And Sufficient

In this paper, we define and investigate a special kind of ruled surfaces called type-2 Smarandache ruled surfaces related to the type-2 Bishop frame in E 3 . From this point and depending on the type-2 Bishop curvature, we provide the necessary and sufficient conditions that allow these surfaces to be developable in a minimal amount of time. Furthermore, an example is given to clear the results.

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