On product affine hyperspheres in Rn+1

被引：3
|
作者：
Xiuxiu Cheng [1 ,2 ]
Zejun Hu [1 ,2 ]
Marilena Moruz [3 ]
Luc Vrancken [3 ,4 ]
机构：
[1] School of Mathematics and Statistics, Zhengzhou University
[2] Henan Key Laboratory of Financial Engineering
[3] Department of Mathematics,KU Leuven
[4] Institut des Sciences et Techniques de Valenciennes (ISTV),Université Polytechnique Hauts de France
来源：
ScienceChina(Mathematics) | 2020年 / 63卷 / 10期
基金：
中国国家自然科学基金;
关键词：
D O I：
暂无
中图分类号：
O186.1 [微分几何];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1which, as Riemannian manifolds, are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvature. As the main result, a complete classification of such affine hyperspheres is established. Moreover, as direct consequences, 3-and 4-dimensional affine hyperspheres with parallel Ricci tensor are also classified.
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页码：2055 / 2078
页数：24
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