On quasi-umbilical locally strongly convex homogeneous affine hypersurfaces

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• 作者：Zejun Hu^a ; ^{huzj@zzu.edu.cn" class="auth_mail} ; Cece Li^b ; ^{ceceli@sina.com" class="auth_mail} ; Chuanjing Zhang^a ; ^{iechjzh@sina.com" class="auth_mail}
• 关键词：53A15 ; 53C30 ; 53C42
• 刊名：Differential Geometry and its Applications
• 出版年：April, 2014
• 年：2014
• 卷：33
• 期：Complete
• 页码：46-74
• 全文大小：450 K

文摘

In this paper, by developing the techniques of F. Dillen and L. Vrancken in , we study quasi-umbilical locally strongly convex homogeneous unimodular-affine hypersurfaces. We will present a characterization of a certain subclass in all dimensions; finally, in dimension five, we will give a complete classification of all quasi-umbilical homogeneous unimodular-affine hypersurfaces.