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A New Version of Bishop Frame and an Application to Spherical Images
Journal of Mathematical Analysis and Applications, 2010 A classical Bishop frame is a moving frame of a curve in Euclidean three space [\textit{R. L. Bishop}, Am. Math. Mon. 82, 246--251 (1975; Zbl 0298.53001)] with the following properties. Considering a curve parametrized by arclength \(s\), the first vector is the unit tangent vector \(T(s)\), the second and third vector \(M_1(s),M_2(s)\) are selected ...
Süha Yılmaz, Melih Turgut
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Bäcklund Transformations According to Bishop Frame in E3/1
Acta Et Commentationes Universitatis Tartuensis De Mathematica, 2015 In this study we have defined Bäcklund transformations of curves according to Bishop frame preserving the natural curvatures under certain assumptions in Minkowski 3-space.
Yilmaz Tuncer, Murat Kemal Karacan
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Characterizations of Tzitzeica curves using Bishop frames
Mathematical Methods in the Applied Sciences, 2021In this study, the conditions of a regular curve to be Tzitzeica curve according to Type‐1 and Type‐2 Bishop frames in Euclidean 3‐space are formulated. Also, the conditions for each Bishop spherical images of a regular curve to be Tzitzeica curves are obtained. Moreover, comprehensive investigations are given for a curve to be a Tzitzeica curve in the
Kemal Eren, Soley Ersoy
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Bishop Frames of Salkowski Curves in E3
Bitlis Eren Üniversitesi Fen Bilimleri DergisiIn this study, alternative, type-1 Bishop, type-2 Bishop and N-Bishop frames of Salkowski curves in E3 are calculated. Moreover, curvatures, Darboux and pol vectors of these frames are found. Also, relationships between the Bishop frames, Darboux vectors and pole vectors are given.
Sümeyye Gur Mazlum
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Bishop Frames and Reference Frames Along the Discretized Curve
2018Two of the three frames associated with an edge of a discretized curve are discussed in this chapter: a Bishop frame and a reference frame. Both of these frames are continually updated as the rod deforms and a pair of rotation operators are used to perform these updates. The operators are known as a space-parallel transport operator and a time-parallel
M. Khalid Jawed +2 more
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Ruled Surfaces According to Bishop Frame in the Euclidean 3-Space
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sakarya Üniversitesi/Eğitim Fakültesi/Matematik Ve Fen Bilimleri Eğitimi Bölümü +4 more
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The Motif of Frames in Elizabeth Bishop's 'In Prison'
2017"'In Prison' is most fully understood in light of Bishop's frames. The concurrent narratives told in 'In Prison' signpost Bishop's lifelong link with Great Village where perhaps, the concept of frames, first originated with her bedroom skylight."
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Canal hypersurfaces according to generalized Bishop frames in 4-space
2022Summary: In the present paper, we study the canal hypersurfaces according to generalized Bishop frames of type B (parallel transport frame), type C and type D in Euclidean 4-space and obtain the Gaussian, mean and principal curvatures of them in general form.
Kazan, Ahmet, Altin, Mustafa
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Generalized Bishop frames of regular curves in $\mathbb{E}^{4}$
Hokkaido Mathematical JournalThe geometry of a regular curve with arc-length parametrization in the Euclidean 3-dimensional space has been classically studied by means of the Frenet frame, which can be understood as an orthonormal moving frame along the curve. The Frenet formulas give the derivatives of the vectors of the Frenet frame with respect to the Frenet frame itself.
Nomoto, Subaru, Nozawa, Hiraku
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Osculating Type Ruled Surfaces With Type-2 Bishop Frame in E3
SymmetryThe aim of this work is to investigate osculating type ruled surfaces with a type 2-Bishop frame in E3. We accomplish this by employing the symmetry of osculating curves. We examine osculating type ruled surfaces by taking into account the curvatures of the base curve.
Suleyman Senyurt +1 more
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