关于一类不定复射影空间中全实类空子流形  

On Totally Real Spacelike Submanifolds of a Class of Indefinite Complex Projective Space

作　　者：郑家耀 宋卫东[1] 

机构地区：[1]安徽师范大学数学计算机科学学院

出　　处：《南通大学学报（自然科学版）》2014年第3期86-89,共4页Journal of Nantong University(Natural Science Edition)　

基　　金：安徽省高等学校优秀青年人才基金项目(2011SQRL021ZD)

摘　　要：利用活动标架法研究了一类不定复射影空间中全实类空子流形,主要结果有3个方面:首先,通过计算和利用Cauchy不等式得到,这类具有平行平均曲率向量的全实类空2-调和子流形成为极大子流形的一个必要条件;其次,通过研究脐性法向量场的位置得到,这类不定复射影空间中的全实全脐类空子流形一定不是法丛平坦的;最后,通过证明一类不定复射影空间中全实伪脐类空子流形的平坦和法丛平坦等价得到,这类子流形一定是极大的.Based on these previous results, three conclusions were obtained through researching the totally real spacelike submanifolds of a class of indefinite complex projective space by using the moving frame method. Firstly, a necessary condition was obtained for the existence of maximal immersions from a totally real spacelike 2-harmonic submanifold into the indefinite complex projective space through the calculation and the Cauchy inequality. Then, it is discovered that the normal bundle of a totally real and totally umbilical spacelike submanifold can′t be at. Finally, it is concluded that one style of totally real pseudo-umbilical spacelike submanifold must be maximal.

关 键 词：不定复射影空间 全实子流形 2-调和 伪脐 

分 类 号：O186.12[理学—数学]