Legendrian dual surfaces in hyperbolic 3-space


Saji K., Yildirim H.

ANNALES POLONICI MATHEMATICI, vol.115, no.3, pp.241-261, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 115 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.4064/ap115-3-4
  • Title of Journal : ANNALES POLONICI MATHEMATICI
  • Page Numbers: pp.241-261

Abstract

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.