Legendrian dual surfaces in hyperbolic 3-space


Saji K., Yildirim H.

ANNALES POLONICI MATHEMATICI, cilt.115, ss.241-261, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 115 Konu: 3
  • Basım Tarihi: 2015
  • Doi Numarası: 10.4064/ap115-3-4
  • Dergi Adı: ANNALES POLONICI MATHEMATICI
  • Sayfa Sayıları: ss.241-261

Özet

We consider surfaces in hyperbolic 3-space and their duals. We study flat dual surfaces in hyperbolic 3-space by using extended Legendrian dualities between pseudo-hyperspheres in Lorentz-Minkowski 4-space. We define the flatness of a surface in hyperbolic 3-space by the degeneracy of its dual, which is similar to the case of the Gauss map of a surface in Euclidean 3-space. Such surfaces are a kind of ruled surfaces. Moreover, we investigate the singularities of these surfaces and the dualities of the singularities.