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

共 50 条

[31] A short note on a class of Weingarten hypersurfaces in Rn+1
de Lima, Eudes L.
GEOMETRIAE DEDICATA, 2021, 213 (01) : 283 - 293
[32] Examples of scalar-flat hypersurfaces in Rn+1
Lira, Jorge H.
Soret, Marc
MANUSCRIPTA MATHEMATICA, 2009, 129 (01) : 55 - 73
[33] RESTRICTION THEOREMS FOR ANISOTROPICALLY HOMOGENEOUS HYPERSURFACES OF Rn+1
Ferreyra, Elida
Urciuolo, Marta
GEORGIAN MATHEMATICAL JOURNAL, 2008, 15 (04) : 643 - 651
[34] On stability of cones in Rn+1 with zero scalar curvature
Barbosa, JLM
Do Carmo, MP
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2005, 28 (02) : 107 - 122
[35] On Stability of Cones in Rn+1 with Zero Scalar Curvature
J. L. M. Barbosa
M. P. Do Carmo
Annals of Global Analysis and Geometry, 2005, 28 : 107 - 122
[36] SOLVING SYSTEMS OF NONLINEAR EQUATIONS IN RN USING A ROTATING HYPERPLANE IN RN+1
GRAPSA, TN
VRAHATIS, MN
BOUNTIS, TC
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1990, 35 (1-4) : 133 - 151
[37] Complete hypersurfaces with bounded mean curvature in Rn+1
Wang, Qiaoling
Xia, Changyu
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2007, 14 (04) : 607 - 619
[38] Singularities of Gauss Map of Pedal Hypersurface in Rn+1
Soliman, M. A.
Abdel-All, Nassar H.
Hassan, Soad A.
Dahi, E.
LIFE SCIENCE JOURNAL-ACTA ZHENGZHOU UNIVERSITY OVERSEAS EDITION, 2011, 8 (04): : 102 - 107
[39] The Fractional Carleson Measures on the Unit Ball of Rn+1
Wang, Dongfang
Ma, Bolin
JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,
[40] Stability of r-minimal cones in Rn+1
Barros, A.
Sousa, P.
JOURNAL OF GEOMETRY AND PHYSICS, 2008, 58 (10) : 1407 - 1416

← 1 2 3 4 5 →