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.

引用

页码：2055 / 2078

页数：24

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