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, vol.33, no.3, pp.751-759, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.35378/gujs.588496
  • Journal Name: Gazi University Journal of Science
  • Journal Indexes: 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)
  • Page Numbers: pp.751-759
  • Keywords: Natural lift, Tangent bundle, Unit dual sphere, Ruled surface, Study's map
  • Ankara Haci Bayram Veli University Affiliated: No

Abstract

© 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.