The horospherical Gauss-Bonnet type theorem in hyperbolic space

被引：24
|
作者：
Izumiya, Shyuichi [1 ]
Romero Fuster, Maria del Carmen
机构：
[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan
[2] Univ Valencia, Dept Geometria & Topol, E-46100 Burjassot, Spain
来源：
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2006年 / 58卷 / 04期
关键词：
hyperbolic space; hypersurfaces; hyperbolic Gauss maps; horospherical geometry; Gauss-Bonnet type theorem;
D O I：
10.2969/jmsj/1179759532
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space and show that totally umbilic hypersurfaces with vanishing curvatures are only horospheres. We also show that the Gauss-Bonnet type theorem holds for the horospherical Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space.
引用
收藏
页码：965 / 984
页数：20
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