Ruled surfaces and tangent bundle of unit 2-sphere of natural lift curves


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Karaca E., ÇALIŞKAN M.

Gazi University Journal of Science, cilt.33, sa.3, ss.751-759, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 3
  • 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
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Hayır

Özet

© 2020, Gazi University Eti Mahallesi. All rights reserved.This article deals with the isomorphism between unit dual sphere, DS2, and the subset of the tangent bundle of unit 2-sphere, TM̅. According to E. Study mapping, a ruled surface in ℝ3 corresponds to each curve on DS2. Through this correspondence, a unique ruled surface in ℝ3 is corresponded to natural lift curve on TM̅. 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.