Legendrian dual surfaces in hyperbolic 3-space

被引：1

作者：

Saji, Kentaro ^{[1
]}

Yildirim, Handan ^{[2
]}

机构：

[1] Kobe Univ, Grad Sch Sci, Dept Math, Nada Ku, Kobe, Hyogo 6578501, Japan

[2] Istanbul Univ, Fac Sci, Dept Math, TR-34134 Istanbul, Turkey

来源：

ANNALES POLONICI MATHEMATICI | 2015年 / 115卷 / 03期

基金：

日本学术振兴会;

关键词：

Lorentz-Minkowski space; Legendrian dualities; hyperbolic; 3-space; singularities; SPACELIKE HYPERSURFACES; FLAT SURFACES; SLANT GEOMETRY; RULED SURFACES; SINGULARITIES; FRONTS; DUALITIES; LIGHTCONE; MANIFOLDS; R-3;

D O I：

10.4064/ap115-3-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：241 / 261

页数：21

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