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

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.