常曲率空间中的具有共形第二基本形式的子流形  

SUBMANIFOLDS WITH CONFORMAL SECOND FUNDAMENTAL FORM IN A CONSTANT CURVATURE SPACE

作　　者：莫小欢[1] 周林峰[1] 

机构地区：[1]北京大学数学科学学院,北京100871

出　　处：《数学年刊（A辑）》2004年第4期407-414,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10171002)

摘　　要：以把调和态射看作等距浸入的单位法投影的问题为背景,研究了具有共形第二基本形式的子流形,论证了具有共形第二基本形式的高维子流形,一般不是由极小点和全脐点构成,这和曲面的情形形成了鲜明的对照。也给出了常曲率空间中具有平行中曲率的奇数维子流形的一个完全分类。Motivated by some issues which enter into harmonic morphisms as unit normal projections of isometric immersions, this paper studies submanifolds with conformal second fundamental form, and demonstrates that high dimensional submanifolds with conformal second fundamental form, are in general not composed of minimal points and totally umbilical points. This contrasts sharply with the situation in surfaces. The authors also give a complete classification of all odd-dimensional these submanifolds with parallel mean curvature in constant curvature spaces.

关 键 词：共形第二基本形式 子流形 常曲率空间 

分 类 号：O189.31[理学—数学]