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


KARACA E., ÇALIŞKAN M.

GAZI UNIVERSITY JOURNAL OF SCIENCE, vol.33, pp.751-759, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33
  • Publication Date: 2020
  • Doi Number: 10.35378/gujs.588496
  • Journal Name: GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Journal Indexes: Emerging Sources Citation Index, 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

Abstract

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.