局部对称仿射超曲面

^Locally Symmetric Affine Hypersurfaces

本文用活动标架法证明了：仿射空间Ａｎ＋１中维数ｎ大于２的非退化超曲面Ｍｎ，相对于诱导的仿射连络局部对称，当且仅当Ｍ是虚（ｉｍｐｒｏｐｅｒ）仿射球或者是非退化的二次超曲面．

Using the method of Moving frames this paper has proved P.Verheyen and L.Verstraelen's Theorem on the locally symmetric affine hypersufaces: Let M be a nondegenerate of An+1 with n>2.Then M is affine locally symmetric w. r. t the induced connection if and only if M is an improper affine hypersphere or a nondegenerate quadratic gypersurface.