摘要
作者证明了如下结果 :设M是空间形式的闭定向Dupin超曲面 ,其截面曲率为正 ,M至少有两个不同主曲率 .如果除最小 (或最大 )主曲率外 ,M的其余主曲率均为常数 ,则最小 (或最大 )主曲率的重数大于 2 .
The author proves the following result. Let M be a closed orientable Dupin hypersurface of a space form. Suppose that the sectional curvature of M>0 and that M has at least two distinct principal curvatures. If all the principal curvatures except the smallest (or the largest) one are constant on M, then the multiplicity of the smallest (or the largest, respectively) principal curvature>2.
出处
《数学杂志》
CSCD
北大核心
2004年第2期182-186,共5页
Journal of Mathematics
关键词
Dupin超曲面
主曲率
重数
Dupin hypersurface
principal curvatures
multiplicity
