Geodesic
Legendrian dual surfaces in hyperbolic 3-space
Kentaro Saji1 ; Handan Yıldırım2
1 Department of Mathematics Graduate School of Science Kobe University Rokko, Nada, Kobe 657-8501, Japan
2 Department of Mathematics Faculty of Science Istanbul University 34134, Vezneciler-Fatih, Istanbul, Turkey
Annales Polonici Mathematici, Tome 115 (2015) no. 3, pp. 241-261.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap115-3-4
Keywords: consider surfaces hyperbolic space their duals study flat dual surfaces hyperbolic space using extended legendrian dualities between pseudo hyperspheres lorentz minkowski space define flatness surface hyperbolic space degeneracy its dual which similar the gauss map surface euclidean space surfaces kind ruled surfaces moreover investigate singularities these surfaces dualities singularities

Kentaro Saji 1 ; Handan Yıldırım 2

1 Department of Mathematics Graduate School of Science Kobe University Rokko, Nada, Kobe 657-8501, Japan
2 Department of Mathematics Faculty of Science Istanbul University 34134, Vezneciler-Fatih, Istanbul, Turkey 
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Kentaro Saji; Handan Yıldırım. Legendrian dual surfaces in hyperbolic 3-space. Annales Polonici Mathematici, Tome 115 (2015) no. 3, pp. 241-261. doi : 10.4064/ap115-3-4. http://geodesic.mathdoc.fr/articles/10.4064/ap115-3-4/

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