Horospherical flat surfaces in Hyperbolic 3-space

被引：49
作者：
Izumiya, Shyuichi [1 ]
Saji, Kentaro [2 ]
Takahashi, Masatomo [3 ]
机构：
[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan
[2] Gifu Univ, Fac Educ, Dept Math, Gifu 5011193, Japan
[3] Muroran Inst Technol, Muroran, Hokkaido 0508585, Japan
来源：
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2010年 / 62卷 / 03期
基金：
日本学术振兴会;
关键词：
hyperbolic; 3-space; horosphere; horospherical geometry; horo-flat surfaces; singularities; GAUSS MAP; SPACE; SINGULARITIES; CURVATURE; HYPERSURFACES; GEOMETRY;
D O I：
10.2969/jmsj/06230789
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently we discovered a new geometry on submanifolds in hyperbolic n-space which is called horospherical geometry. Unfortunately this geometry is not invariant under the hyperbolic motions (it is invariant under the canonical action of SO(n)), but it has quite interesting features. For example, the flatness in this geometry is a hyperbolic invariant and the total curvatures are topological invariants. In this paper, we investigate the horospherical flat surfaces (flat surfaces in the sense of horospherical geometry) in hyperbolic 3-space. Especially, we give a generic classification of singularities of such surfaces. As a consequence, we can say that such a class of surfaces has quite a rich geometric structure.
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收藏
页码：789 / 849
页数：61
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