摘要
设为ｎ＋ｐ＋ｑ维欧氏空间Ｅｎ＋ｐ＋ｑ中具有平行中曲率向量的ｎ＋ｐ维伪脐子流形，Ｍｎ为的ｎ维子流形。本文得到Ｍｎ在中为极小子流形的充要条件；并指出著名的Ｔａｋａｈａｓｈｉ公式是其特例。
Let be a submanifold of eculidian space with parallel mean curvature vector,and Mn a submanifold of.A sufficient and necessary condition that Mn is the minimal submanifold of is set up in this article.The famours Takahashi Theorem is the special case of this condition.
出处
《长沙交通学院学报》
1994年第3期1-5,共5页
Journal of Changsha Communications University
关键词
极小
子流形
充要条件
伪脐子流形
minimal
submanifolds
necessary and sufficient condition
pseudo-umbilicalsubmanifold
parallel mean curvature vector
