On space-like constant slope surfaces and bertrand curves in minkowski 3-space

BABAARSLAN M., YAYLI Y.

Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, cilt.63, sa.F2, ss.323-339, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63 Sayı: F2
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1515/aicu-2015-0009
  • Dergi Adı: Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.323-339
  • Anahtar Kelimeler: Bertrand curve, Helix, Lorentzian Sabban frame, Pseudo-spherical Darboux images, Pseudo-spherical evolutes, Space-like constant slope surface
  • Ankara Üniversitesi Adresli: Evet

Özet

© 2017, Sciendo. All rights reserved.In the present paper, we define the notions of Lorentzian Sabban frames and de Sitter evolutes of the unit speed space-like curves on de Sitter 2-space (formula presented). In addition, we investigate the invariants and geometric properties of these curves. Afterwards, we show that space-like Bertrand curves and time-like Bertrand curves can be constructed from unit speed space-like curves on de Sitter 2-space (formula presented) and hyperbolic space ℍ2, respectively. We obtain the relations between Bertrand curves and helices. Also we show that pseudo-spherical Darboux images of Bertrand curves are equal to pseudo-spherical evolutes in Minkowski 3-space (formula presented). Moreover we investigate the relations between Bertrand curves and space-like constant slope surfaces in (formula presented). Finally, we give some examples to illustrate our main results.