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个人信息Personal Information
教授
博士生导师
硕士生导师
性别：男
毕业院校：吉林大学
学位：博士
所在单位：数学科学学院
学科：基础数学
联系方式：ximinliu@dlut.edu.cn
电子邮箱：ximinliu@dlut.edu.cn
Complete space-like hypersurfaces with constant scalar curvature
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论文类型：期刊论文
发表时间：2001-07-01
发表刊物：MANUSCRIPTA MATHEMATICA
收录刊物：Scopus、SCIE
卷号：105
期号：3
页面范围：367-377
ISSN号：0025-2611
摘要：Let M-n be a complete space-like hypersurface with constant normalized scalar curvature R in the de Sitter space S-1(n+1) and denote (R) over bar = 1 - R. We prove that if the norm square \h\(2) of the second fundamental form of M-n satisfies n (R) over bar less than or equal to sup \h\(2) less than or equal to n/(n-2)(n (R$) over bar -2)[n(n - 1)(R) over bar (2) - 4(n - 1)(R) over bar + n], then either sup \h\(2) = n (R) over bar and M-n is a totally umbilical hypersurface; or sup \h\(2) = n/(n-2)(n (R) over bar -2)[n(n - 1)(R) over bar (2) - 4(n - 1)(R) over bar + n], and, up to rigid motion, M-n is a hyperbolic cylinder H-1(1 - coth(2) r) X Sn-1(1 - tanh(2) r).