Characterizations of the Calabi product of hyperbolic affine hyperspheres

被引：31

作者：

Hu, Zejun ^{[1
]}

Li, Haizhong ^{[2
]}

Vrancken, Luc ^{[3
]}

机构：

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[3] Univ Valenciennes, LAMATH, ISTV2, F-59313 Valenciennes 9, France

来源：

RESULTS IN MATHEMATICS | 2008年 / 52卷 / 3-4期

关键词：

affine hypersphere; Calabi product; affine hypersurface;

D O I：

10.1007/s00025-008-0312-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

There exists a well known construction which allows to associate with two hyperbolic affine hyperspheres fi : M-i(ni) -> Rni+1 a new hyperbolic affine hypersphere immersion of I x M-1 x M-2 into Rn1+n2+2. In this paper we deal with the inverse problem: how to determine from properties of the difference tensor whether a given hyperbolic a. ne hypersphere immersion of a manifold M-n -> Rn+1 can be decomposed in such a way.

引用

页码：299 / 314

页数：16

共 20 条

[1]

BOLTON J, P EDINBURGH IN PRESS

[2]

Calabi E., 1972, Symposia Mathematica., P19

[3] SOME PINCHING AND CLASSIFICATION-THEOREMS FOR MINIMAL SUBMANIFOLDS [J].

CHEN, BY .

ARCHIV DER MATHEMATIK, 1993, 60 (06) :568-578

[4] COMPLETE AFFINE HYPERSURFACES .1. THE COMPLETENESS OF AFFINE METRICS [J].

CHENG, SY ;

YAU, ST .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1986, 39 (06) :839-866

[5] CONJUGATE CONNECTIONS AND RADON THEOREM IN AFFINE DIFFERENTIAL GEOMETRY [J].

DILLEN, F ;

NOMIZU, K ;

VRANKEN, L .

MONATSHEFTE FUR MATHEMATIK, 1990, 109 (03) :221-235

[6] CALABI-TYPE COMPOSITION OF AFFINE SPHERES [J].

DILLEN, F ;

VRANCKEN, L .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 1994, 4 (04) :303-328

[7] INTERNAL CHARACTERIZATION OF DISTORTED PRODUCTS [J].

HIEPKO, S .

MATHEMATISCHE ANNALEN, 1979, 241 (03) :209-215

[8]

HU Z, DIFF GEOM A IN PRESS

[9] Lorentzian affine hyperspheres with constant affine sectional curvature [J].

Kriele, M ;

Vrancken, L .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (04) :1581-1599

[10] An extremal class of three-dimensional hyperbolic affine spheres [J].

Kriele, M ;

Vrancken, L .

GEOMETRIAE DEDICATA, 1999, 77 (03) :239-252

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