Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves

KARACA E., ÇALIŞKAN M.

GAZI UNIVERSITY JOURNAL OF SCIENCE, cilt.33, ss.751-759, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33
  • Basım Tarihi: 2020
  • Doi Numarası: 10.35378/gujs.588496
  • Dergi Adı: GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, Metadex, Civil Engineering Abstracts, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.751-759
  • Anahtar Kelimeler: Natural lift, Tangent bundle, Unit dual sphere, Ruled surface, Study's map
  • Gazi Üniversitesi Adresli: Evet

Özet

This article deals with the isomorphism between unit dual sphere, DS2, and the subset of the tangent bundle of unit 2-sphere, T (M) over bar. According to E. Study mapping, a ruled surface in R-3 corresponds to each curve on DS2. Through this correspondence, a unique ruled surface in R-3 is corresponded to natural lift curve on T (M) over bar. Then striction curve, shape operator, mean curvature and Gaussian curvature of these ruled surfaces obtained by the natural lift curves are calculated. Developabilitiy condition of these ruled surfaces is given. Finally, we give an example to support the main results.