Ruled surfaces and tangent bundle of unit 2-sphere

Hathout F., Bekar M., Yayli Y.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.14, sa.10, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 10
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s0219887817501456
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Tangent bundle, Legendre curve, unit dual sphere, Study's map, ruled surface, sriction curve
  • Gazi Üniversitesi Adresli: Hayır

Özet

In this paper, a one-to-one correspondence is given between the tangent bundle of unit 2-sphere, TS2, and the unit dual sphere, S-D(2). According to Study's map, to each curve on S-D(2) corresponds a ruled surface in Euclidean 3-space, R-3. Through this correspondence, we have corresponded to each curve on TS2 a unique ruled surface in R-3. Moreover, the relationships between the developability conditions of these ruled surfaces and their striction curves are analyzed. It is shown that the ruled surfaces corresponding to the involute-evolute curve couples on TS2 are developable.