Legendrian dual surfaces in hyperbolic 3-space

• Autorzy: Kentaro Saji , Handan Yıldırım
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
• 53B30: Lorentz metrics, indefinite metrics
• 53A35: Non-Euclidean differential geometry
• 57R45: Singularities of differentiable mappings
• 58K99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 115
• Numer: 3
• Strony: 241-261

Daty

wydano

2015

Twórcy

autor

Kentaro Saji

• Department of Mathematics, Graduate School of Science, Kobe University, Rokko, Nada, Kobe 657-8501, Japan

autor

Handan Yıldırım

• Department of Mathematics, Faculty of Science, Istanbul University, 34134, Vezneciler-Fatih, Istanbul, Turkey

Identyfikatory

DOI

10.4064/ap115-3-4