| 张远征.静态AdS时空中的常平均曲率类空超曲面[J].数学年刊A辑,2009,30(6):829~838 |
| 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 |
| Received:September 08, 2008 Revised:December 31, 2008 |
| DOI： |
| 中文关键词: Einstein度量, 离差函数, 积分公式, 扭积 |
| 英文关键词:Einstein metric, Deviation function, Integral formulas, Warped product |
| 基金项目: |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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