摘要
设x:Mn→Sn+1是(n+1)-维单位球面上不含脐点的超曲面,在Sn+1的Mbius交换群下浸入x的四个基本不变量是:一个黎曼度量g称为Mbius度量;一个1-形式Φ称为Mbius形式;一个对称的(0,2)张量A称为Blaschke张量和一个对称的(0,2)张量B称为Mbius第二基本形式。对称的(0,2)张量D=A+λB也是Mbius不变量,其中λ是常数,D称为x的仿Blaschke张量,李海中和王长平研究了满足条件:(ⅰ)Φ=0;(ⅱ)A+λB+μg=0的超曲面,其中λ和μ都是函数,他们证明了λ和μ都是常数,并且给出了这类超曲面的分类,也是在Φ=0的条件下D只有一个互异的特征值的超曲面的分类。对S6上满足如下条件的超曲面进行了分类:(ⅰ)Φ=0;(ⅱ)对某常数λ,D具有3个互异的常数特征值。
Let x.Mn--S＂＋1 be a hypersurface in the （n＋ 1）-dimensional unit sphere Sn-}-1 without umbilics. There are four basic invariants of x under the MObius transformation group in Sn＋l , i. e. , a Riemannian metric g called M6bius metric,a 1-form called M6bius form,a symmetric （0,2） tensor A called Blaschke tensor and symmetric （0,2） tensor B called MObius second fundamental form. Let D=A＋.B ,where is a constant,therefore D becomes a symmetric （0,2） tensor and a M？ bius invariant. D is also called Pata- blasschke tensor of x. Li and Wang have studied the hypersurfaces x：Mn--Sn＋ ,which satisfy： （i）@=0 （ii） A-k）,B＋,ug=O for some functions , and/z on M. Theyproved that , and should be constants. In fact, they classified the hypersurfaces which satisfy.（i）= 0 , （ii）D had only one distinct constant eigenvalue. In this paper,We classified the hypersurfaces x.MS--S6 ,which satisfied. （i）q=O x（ii）D has exactly three distinct constant para-Blaschke eigenvalues for some constant A.
出处
《南昌大学学报（理科版）》
CAS
北大核心
2013年第2期131-139,共9页
Journal of Nanchang University(Natural Science)
