【摘要】 设x:M→Sⁿ⁺¹是（n+1）-维单位球面上不含脐点的超曲面,在Sⁿ⁺¹的Moebius变换群下浸入x的四个基本不变量是:一个黎曼度量g称为Moebius度量;一个1-形式Φ称为Moebius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Moebius第二基本形式.对称的（0,2）张量D=A+λB也是Moebius不变量,其中λ是常数,D称为浸入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,也就是在Φ=0的条件下D只有一个互异的特征值的超曲面的分类.本文对S⁵上满足如下条件的超曲面进行了完全分类:（i）Φ=0,（ii）对某常数λ,D具有常数特征值.更多还原

【Abstract】 Let x:Mⁿ→Sⁿ⁺¹ be a hypersurface in the（n+ 1）-dimensional unit sphere Sⁿ⁺¹ without umbilics.Four basic invariants of x under the Moebius transformation group in Sⁿ⁺¹ are a Riemannian metric g called Moebius metric,a 1-formΦcalled Moebius form,a symmetric（0,2） tensor A called Blaschke tensor and symmetric（0,2） tensor B called Moebius second fundamental form.Let D = A +λB,whereλis a constant.Then D is a symmetric（0,2） tensor and a Moebius invariant.D is called Para-Blaschke 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 functionsλandμon M; they have proved thatλandμmust be constants and have classified the hypersurfaces; in fact,they have classified the hypersurfaces which satisfy:（i）Φ= 0,（ii） D has only one distinct constant eigenvalue.In this paper,We classify the hypersurfaees x:M→S⁵,which satisfy:（i）Φ= 0,（ii） D has constant eigenvalues for some constantsλ.更多还原