Integral geometry and the Gauss-Bonnet theorem in constant curvature spaces

被引：31
|
作者：
Solanes, G [1 ]
机构：
[1] Univ Stuttgart, Inst Geometrie & Topol, D-70569 Stuttgart, Germany
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 358卷 / 03期
关键词：
integral geometry; total curvature;
D O I：
10.1090/S0002-9947-05-03828-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give an integral-geometric proof of the Gauss-Bonnet theorem for hypersurfaces in constant curvature spaces. As a tool, we obtain variation formulas in integral geometry with interest in its own.
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页码：1105 / 1115
页数：11
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