On locally strongly convex affine hypersurfaces with parallel cubic form. Part I

被引：32
作者：
Hu, Zejun [1 ]
Li, Haizhong [4 ]
Simon, Udo [2 ]
Vrancken, Luc [3 ]
机构：
[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China
[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany
[3] Univ Valenciennes, LAMATH, ISTV2, Valenciennes, France
[4] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2009年 / 27卷 / 02期
关键词：
Affine hyperspheres; Parallel cubic Pick form; Einstein Blaschke metric; DIFFERENTIAL GEOMETRY; SURFACES; HYPERSPHERES; SPHERES;
D O I：
10.1016/j.difgeo.2008.10.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study locally strongly convex affine hypersurfaces of Rn+1 that have parallel cubic form with respect to the Levi-Civita connection of the affine Berwald-Blaschke metric: it is known that they are affine spheres. In dimension n <= 7 we give a complete classification of such hypersurfaces; in particular, we present new examples of affine spheres. (C) 2008 Elsevier B.V. All rights reserved.
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收藏
页码：188 / 205
页数：18
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