| SPACELIKE SUBMANIFOLDS IN THE DE SITTER SPACE Sp^（n＋p）（c）WITH CONSTANT SCALAR CURVATURE |
| |
| 引用本文： | ZhangJianfeng. SPACELIKE SUBMANIFOLDS IN THE DE SITTER SPACE Sp^（n＋p）（c）WITH CONSTANT SCALAR CURVATURE[J]. 高校应用数学学报(英文版), 2005, 20(2): 183-196. DOI: 10.1007/s11766-005-0051-3 |
| |
| 作者姓名： | ZhangJianfeng |
| |
| 作者单位： | Dept.ofMath.,ZhejiangUniv.,Hangzhou310028,China |
| |
| 摘 要： | Let M^n be a closed spacelike submanifold isometrically immersed in de Sitter space Sp^(n p)(c)， Denote by R,H and S the normalized scalar curvature,the mean curvature and the square of the length of the second fundamental form of M^n ,respectively. Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for M^n immersed in Sp^(n p)(c) with parallel normalized mean curvature vector field is proved. When n≥3, the pinching constant is the best. Thus, the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature”(see Manus Math, 1998,95 :499-505) is corrected. Moreover,the reduction of the codimension when M^n is a complete submanifold in Sp^(n p)(c) with parallel normalized mean curvature vector field is investigated.
|
| 关 键 词： | 类空间子流形 常量曲率 平行正则 边量场 Sitter空间 |
| 收稿时间： | 2004-06-02 |
Spacelike submanifolds in the de Sitter space Spn+p(c) with constant scalar curvature |
| |
| Zhang Jianfeng. Spacelike submanifolds in the de Sitter space Spn+p(c) with constant scalar curvature[J]. Applied Mathematics A Journal of Chinese Universities, 2005, 20(2): 183-196. DOI: 10.1007/s11766-005-0051-3 |
| |
| Authors: | Zhang Jianfeng |
| |
| Affiliation: | (1) Dept. of Math., Zhejiang Univ., 310028 Hangzhou, China |
| |
| Abstract: | Let M n be a closed spacelike submanifold isometrically immersed in de Sitter space S p n+p (c). Denote by R, H and S the normalized scalar curvature, the mean curvature and the square of the length of the second fundamental form of M n, respectively. Suppose R is constant and R≤c. The pinching problem on S is studied and a rigidity theorem for M n immersed in S p n+p (c) with parallel normalized mean curvature vector field is proved. When n≥3, the pinching constant is the best. Thus, the mistake of the paper “Space-like hypersurfaces in de Sitter space with constant scalar curvature” (see Manus Math, 1998, 95:499s-505) is corrected. Moreover, the reduction of the codimension when M n is a complete submanifold in S p n+p (c) with parallel normalized mean curvature vector field is investigated. |
| |
| Keywords: | 53C42 53C40 |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
|
