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静态AdS时空中的常平均曲率类空超曲面

Space-Like Hypersurfaces with Constant Mean Curvature in Static AdS Space-Times
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摘要 在n+1维静态AdS时空M中,利用双扭结构建立了一些积分公式,并利用这些积分公式证得:如果M的Ricci曲率具有非负离差,那么以n-1维圆球面为边界的常平均曲率类空超曲面必为测地圆盘(h=0)或全脐盖(h≠0).作为推论,对于离差为零的Einstein静态AdS时空,结论也真. The author constructs some integral formulas for space-like hypersurfaces in the static AdS space-times, and uses them to show that only the geodesic n-disc and the umbilical caps in the static AdS space-times, with non-negative deviation, are the space-like hypersurfaces with constant mean curvatures which are bounded by an (n-1)-round sphere.As a corollary, it holds for static AdS space-times with Einstein metric.
作者 张远征
出处 《数学年刊(A辑)》 CSCD 北大核心 2009年第6期829-838,共10页 Chinese Annals of Mathematics
基金 上海财经大学211工程三期重点学科建设基金资助的项目
关键词 EINSTEIN度量 离差函数 积分公式 扭积 Einstein metric, Deviation function, Integral formulas, Warped product
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参考文献7

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