The author studied centroaffine hypersurfaces in (n+1) dimensional Euclidean space R n+1 and obtained the results for the uniqueness and existence of centroaffine hypersurfaces.
本文作者研究了 (n + 1)维欧氏空间Rn+1中的中心仿射超曲面 ,得到了中心仿射超曲面的唯一性和存在性两个结
In this paper, we will first introduce connection form g and cubic form A, then westudied centroaffine hypersurfaces in (n + 1) -dimensional affinespace An+1 and got the uniqueness and existence of centroaffinehypersurfaces.
对任意超曲面浸入x:M→A~(n+1),若位置矢量x横截于点x处的切平面x_*(TM),则TM上存在在中心仿射变换群G作用下不变的对称的双线性形式g和对称的三次协变形式A,如果g非退化,我们则称x为中心仿射超曲面。
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