RULED SURFACES AND TANGENT BUNDLE OF PSEUDO-SPHERE OF NATURAL LIFT CURVES

Karaca E., Mustafa M.

JOURNAL OF SCIENCE AND ARTS, no.3, pp.573-586, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2020
  • Doi Number: 10.46939/j.sci.arts-20.3-a07
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.573-586
  • Keywords: tangent bundle, ruled surface, natural lift curve, study's map
  • Gazi University Affiliated: Yes

Abstract

In this article, firstly, the isomorphism between the subset of the tangent bundle of Lorentzian unit sphere, T (M) over tilde, and Lorentzian unit sphere, S-1(2) is represented. Secondly, the isomorphism between the subset of hyperbolic unit sphere, T (M) over cap, and hyperbolic unit sphere, H-2 is given. According to E. Study mapping, any curve on S-1(2) or H-2 corresponds to a ruled surface in R-1(3). By constructing these isomorphisms, we correspond to any natural lift curve on T (M) over tilde or T (M) over cap a unique ruled surface in R-1(3). Then we calculate striction curve, shape operator, Gaussian curvature and mean curvature of these ruled surfaces. We give developability condition of these ruled surfaces. Finally, we give examples to support the main results.