On product affine hyperspheres in R^n+1

作     者：Xiuxiu Cheng Zejun Hu Marilena Moruz Luc Vrancken Xiuxiu Cheng;Zejun Hu;Marilena Moruz;Luc Vrancken

作者机构：School of Mathematics and StatisticsZhengzhou UniversityZhengzhou 450001China Henan Key Laboratory of Financial EngineeringZhengzhou 450001China Department of MathematicsKU LeuvenLeuven 3001Belgium Institut des Sciences et Techniques de Valenciennes(ISTV)Universit´e Polytechnique Hauts de FranceValenciennes 59313France 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2020年第63卷第10期

页      面：2055-2078页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China(Grant No.11771404) 

主　　题：affine hypersurface affine metric affine hypersphere Levi-Civita connection constant sectional curvature parallel Ricci tensor 

摘      要：In this paper,we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1 which,as Riemannian manifolds,are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional *** the main result,a complete classification of such affine hyperspheres is ***,as direct consequences,3-and 4-dimensional affine hyperspheres with parallel Ricci tensor are also classified.