scholarly journals Investigating Spherical Images of a Curve According to Type-1 Bishop Frame in Weyl Space Using Prolonged Covariant Derivative

2021 ◽  
Author(s):  
Nil KOFOGLU
Keyword(s):  
Covariant Derivative ◽  
Bishop Frame ◽  
Weyl Space ◽  
Spherical Images

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.

scholarly journals Kählerian submanifolds in a complex projective space with second fundamental form of polynomial type

1984 ◽  
Vol 96 ◽  
pp. 61-70
Author(s):  
Ryoichi Takagi
Keyword(s):  
Projective Space ◽  
Sectional Curvature ◽  
Covariant Derivative ◽  
Complex Projective Space ◽  
Second Fundamental Form ◽  
Holomorphic Sectional Curvature ◽  
Fundamental Tensor ◽  
Polynomial Type ◽  
Complex Projective

Let PN be an iV-dimensional complex projective space with Fubini-Study metric of constant holomorphic sectional curvature, and M be a Kählerian submanifold in PN. Let H be the second fundamental tensor + of M, and be the covariant derivative of type (1, 0) on M.

An application of N-Bishop frame to spherical images for direction curves

2017 ◽  
Vol 14 (11) ◽  
pp. 1750162 ◽  
Author(s):  
Ozgur Keskin ◽  
Yusuf Yayli
Keyword(s):  
Unit Sphere ◽  
Integral Curve ◽  
Normal Direction ◽  
Bishop Frame ◽  
Integral Curves ◽  
Spherical Images

In this paper, we first introduce [Formula: see text]-Bishop frame for a normal direction curve which is defined as an integral curve of the principal normal of a curve. We express this new frame and its properties. Afterwards, we obtain new spherical images by translating [Formula: see text]-Bishop frame vectors to the center of unit sphere [Formula: see text] in [Formula: see text]. Then, these new spherical images are called [Formula: see text]-Bishop spherical images. Additionally, we compute the Frénet–Serret equations of these new spherical images. Moreover, we show that integral curves of [Formula: see text]-Bishop spherical images of slant helices are also slant helices. Finally, we present some illustrated examples.

scholarly journals Cusps of Bishop Spherical Indicatrixes and Their Visualizations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Haiming Liu ◽  
Donghe Pei
Keyword(s):  
Space Curve ◽  
Singular Points ◽  
Bishop Frame ◽  
Spherical Images

The main result of this paper is using Bishop Frame and “Type-2 Bishop Frame” to study the cusps of Bishop spherical images and type-2 Bishop spherical images which are deeply related to a space curve and to make them visualized by computer. We find that the singular points of the Bishop spherical images and type-2 Bishop spherical images correspond to the point where Bishop curvatures and type-2 Bishop curvatures vanished and their derivatives are not equal to zero. As applications and illustration of the main results, two examples are given.

New models of normal motions of the inextensible curves according to type-1 Bishop frame in ℝ3

2020 ◽  
Vol 18 (01) ◽  
pp. 2150009
Author(s):  
Samah Gaber Mohamed
Keyword(s):  
Time Evolution ◽  
Evolution Equations ◽  
Sufficient Condition ◽  
Frenet Frame ◽  
Comparison Study ◽  
Necessary And Sufficient Condition ◽  
Bishop Frame ◽  
New Models ◽  
Necessary And Sufficient

In this work, we compute the time evolution equations (TEEs) of the type-1 Bishop frame of the curve. Also, we study the time evolution equations for type-1 Bishop curvatures (TEEBCs) as a system of partial differential equations (PDEs). Through this study, we give a necessary and sufficient condition for the normal and binormal Bishop velocities. Also, we construct new models of normal motions of inextensible curves in [Formula: see text]. These models are constructed for curves that move according to the type-1 Bishop frame. Also, we make a comparison study between surfaces obtained by the motions of inextensible curves according to the two frames, the type-1 Bishop frame and the Frenet frame.

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