具有共变对称张量场的仿射超曲面

Affine Hypersurfaces with Covariant-Symmetric Tensor Fields

用活动标架法从不同方面证明并推广了文[2]的结果：（1）若Mn（n≥2）是n＋1维仿射空间An+1中非退化的仿射超曲面，则2S共变对称（或R·S=0），当且仅当M是仿射球；（2）若Mn（n≥2）是An+1中非退化的仿射起曲面，则K共变对称当且仅当M是仿射球；若K和K都共变对称，则M是仿球，且J=0和仿射度量G是Einstein度量．

Using the mathod of Moving Frames,this paper has proved the following theorems: (1)Let Mn (u≥2) be a nondegenerate affine hypersurface in the affine spare An+1, then 2S is covariant-Symmetric (orR. S=0) if and only if M is an affine hypersphere; (2) Let Mn(n≥2) be a nondegenerate affine hypersurfacein An+1,then K is covarant-Symmetric if and only if M is an affine hypersphere; If K and K are both covariant-Symmetric, then M is an affine hypersphere with J=0 and its affine metric G is an Einstein metric.