On four-dimensional Einstein affine hyperspheres
On four-dimensional Einstein affine hyperspheres
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DOI：
10.1016/j.difgeo.2016.10.003
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发表时间：
2017-02
影响因子：
0.5
通讯作者：
Zejun Hu;Haizhong Li;L. Vrancken
中科院分区：
文献类型：
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作者：
Zejun Hu;Haizhong Li;L. Vrancken
Vrancken-Li-Simon对Rn + 1中仿射度量为常截面曲率的局部强凸仿射超球进行了分类，但对n维仿射度量为Einstein的局部强凸仿射超球进行分类仍然是一个难题.本文解决了n= 4时的问题。
It is well-known that Vrancken–Li–Simon classified locally strongly convex affine hyperspheres in R n+ 1 whose affine metric are of constant sectional curvatures, but on the other side it is still a difficult problem to classify n-dimensional locally strongly convex affine hyperspheres whose affine metrics are Einstein. In this paper, we have solved the problem in case n= 4.