LINEAR WEINGARTEN SPACELIKE HYPERSURFACES IN LOCALLY SYMMETRIC LORENTZ SPACE

被引：4

作者：

Yang, Dan ^{[1
]}

机构：

[1] Shenyang Univ, Coll Sci, Shenyang 110044, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2012年 / 49卷 / 02期

关键词：

linear Weingarten; spacelike hypersurface; locally symmetric; CONSTANT SCALAR CURVATURE; MEAN-CURVATURE; SITTER SPACE; RIGIDITY THEOREMS; DESITTER SPACE;

D O I：

10.4134/BKMS.2012.49.2.271

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a linear Weingarten spacelike hypersurface in a locally symmetric Lorentz space with R = aH + b, where R and H are the normalized scalar curvature and the mean curvature, respectively. In this paper, we give some conditions for the complete hypersurface M to be totally umbilical.

引用

页码：271 / 284

页数：14

共 21 条

[1]

Abe N., 1987, YOKOHAMA MATH J, V35, P123

[2] ON SPACELIKE HYPERSURFACES WITH CONSTANT MEAN-CURVATURE IN THE DE SITTER SPACE [J].

AKUTAGAWA, K .

MATHEMATISCHE ZEITSCHRIFT, 1987, 196 (01) :13-19

[3] Complete space-like hypersurfaces in locally symmetric Lorentz spaces [J].

Baek, JO ;

Cheng, QM ;

Suh, YJ .

JOURNAL OF GEOMETRY AND PHYSICS, 2004, 49 (02) :231-247

[4] Complete hypersurfaces with constant scalar curvature in spheres [J].

Brasil, Aldir, Jr. ;

Gervasio Colares, A. ;

Palmas, Oscar .

MONATSHEFTE FUR MATHEMATIK, 2010, 161 (04) :369-380

[5] Rigidity theorems for complete spacelike hypersurfaces with constant scalar curvature in De Sitter space [J].

Camargo, F. E. C. ;

Chaves, R. M. B. ;

Sousa, L. A. M., Jr. .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2008, 26 (06) :592-599

[6] A rigidity theorem for complete CMC hypersurfaces in Lorentz manifolds [J].

Caminha, A. .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2006, 24 (06) :652-659

[7]

Cheng Q. M., 1990, MEM FS KYUSHU U A, V44, P67

[8]

Cheng QM, 1998, MANUSCRIPTA MATH, V95, P499

[9] REMARKS ON EXISTENCE OF SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE [J].

GODDARD, AJ .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1977, 82 (NOV) :489-495

[10] LINEAR WEINGARTEN HYPERSURFACES IN A UNIT SPHERE [J].

Li, Haizhong ;

Suh, Young Jin ;

Wei, Guoxin .

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2009, 46 (02) :321-329

← 1 2 3 →