Legendrian dual surfaces in hyperbolic 3-space

Volume 115 / 2015

Kentaro Saji, Handan Yıldırım Annales Polonici Mathematici 115 (2015), 241-261 MSC: Primary 53A35; Secondary 53B30, 57R45, 53C42, 58K99. DOI: 10.4064/ap115-3-4


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.


  • Kentaro SajiDepartment of Mathematics
    Graduate School of Science
    Kobe University
    Rokko, Nada, Kobe 657-8501, Japan
  • Handan YıldırımDepartment of Mathematics
    Faculty of Science
    Istanbul University
    34134, Vezneciler-Fatih, Istanbul, Turkey

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