SPACELIKE SUBMANIFOLDS IN THE DE SITTER SPACE Sp^(n+p)(c)WITH CONSTANT SCALAR CURVATURE |
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作者姓名: | ZhangJianfeng |
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作者单位: | Dept.ofMath.,ZhejiangUniv.,Hangzhou310028,China |
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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.
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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: | 2 June 2004 |
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