Canonical equiaffine hypersurfaces in ℝn+1
Canonical equiaffine hypersurfaces in ℝn+1
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DOI：
10.1007/bf02572426
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发表时间：
1993-09
影响因子：
0.8
通讯作者：
Changping Wang
中科院分区：
文献类型：
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作者：
Changping Wang
仿射微分几何中的一个重要问题是对具有常截面曲率Btaschke度量的仿射超球进行分类。这个问题近年来得到了广泛的研究。由于Radon [14]，Li和Penn [8]，Magid和Ryan [9]和Simon [17]的工作，在第二维中进行了分类。Li [7]给出了关于具有正定Blaschke度量的局部仿射超球的第一个高维结果，他证明了具有零数量曲率的仿射超球是由下式定义的超球的椭圆抛物面或仿射等价：
An important problem in affine differential geometry is to classify all the affine hyperspheres with constant sectional curvature (abbreviated CSC) Btaschke metric. This problem has been extensively studied in the recent years. The classification has been made in dimension 2 due to works of Radon [14], Li and Penn [8], Magid and Ryan [9] and Simon [17]. The first result in high dimension for local affine hyperspheres with positive definite Blaschke metric was given by Li [7], who proved that an affine hypersphere with vanishing scalar curvature is either the elliptic paraboloid or affinely equivalent to the hypersphere defined by