【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Mbius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Mbius度量;一个1-形式Φ称为Mbius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Mbius第二基本形式。对称的(0,2)张量D=A+λB也是Mbius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。更多还原

【Abstract】 Let x:Mn→Sn+1 be a hypersurface in the(n+1)-dimensional unit sphere Sn+1 without umbilics.There are four basic invariants of x under the Mbius transformation group in Sn+1,i.e.,a Riemannian metric g called Mbius metric,a 1-form Φ called Mbius form,a symmetric(0,2) tensor A called Blaschke tensor and symmetric(0,2) tensor B called Mbius second fundamental form.Let D=A+λB,where λ is a constant,therefore D becomes a symmetric(0,2) tensor and a M?bius invariant.D is also called Patablasschke tensor of x.Li and Wang have studied the hypersurfaces x:Mn→Sn+1,which satisfy:(i)Φ=0;(ii) A+λB+μg=0 for some functions λ and μ on M.Theyproved that λ and μ should be constants.In fact,they classified the hypersurfaces which satisfy:(i)Φ=0,(ii)D had only one distinct constant eigenvalue.In this paper,We classified the hypersurfaces x:M5→S6,which satisfied:(i)Φ=0;(ii)D has exactly three distinct constant para-Blaschke eigenvalues for some constant λ.更多还原