A new version of Bishop frame and an application to spherical images
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.371, sa.2, ss.764-776, 2010 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 371 Sayı: 2
- Basım Tarihi: 2010
- Doi Numarası: 10.1016/j.jmaa.2010.06.012
- Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.764-776
- Anahtar Kelimeler: Classical differential geometry, Spherical images, Bishop frame, General helix, Slant helix, Euclidean space
- Dokuz Eylül Üniversitesi Adresli: Evet
Özet
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. (C) 2010 Elsevier Inc. All rights reserved.