Addendum to the paper: Sphere theorem by means of the ratio of mean curvature functions
Addendum to the paper: Sphere theorem by means of the ratio of mean curvature functions
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DOI：
10.1017/s0017089501020110
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发表时间：
2001-05
影响因子：
0.5
通讯作者：
Sung-Eun Koh;Seung-won Lee
中科院分区：
文献类型：
--
作者：
Sung-Eun Koh;Seung-won Lee
证明了n维无边界紧致定向流形在n+1维欧氏空间、双曲空间或开半球中的浸入是全脐浸入，如果其中一个平均曲率函数H_l不为零，且H_k/H_l之比为常数，l\leq k，l \leq n，k\ne l.
It is shown that an immersion of n dimensional compact oriented manifold without boundary into the n+1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilic immersion if one of the mean curvature function H_l does not vanish and the ratio H_k/H_l is constant, 1\leq k, l \leq n, k\ne l.