A new version of Bishop frame and an application to spherical images |
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Authors: | Süha Y?lmaz |
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Institution: | Dokuz Eylül University, Buca Educational Faculty, Department of Mathematics, 35160, Buca-Izmir, Turkey |
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Abstract: | In this work, we introduce a new version of Bishop frame using a common vector field as binormal vector field of a regular curve and call this frame as “Type-2 Bishop Frame”. Thereafter, by translating type-2 Bishop frame vectors to the center of unit sphere of three-dimensional Euclidean space, we introduce new spherical images and call them as type-2 Bishop spherical images. Frenet-Serret apparatus of these new spherical images are obtained in terms of base curve's type-2 Bishop invariants. Additionally, we express some interesting relations and illustrate two examples of our main results. |
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Keywords: | Classical differential geometry Spherical images Bishop frame General helix Slant helix Euclidean space |
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