Remarks on Complete Spacelike Hyper-surfaces with Constant Mean Curvature in the de Sitter Space

摘要

Let M be an n(≥3)-dimensional completely non-compact spacelike hypersurface in the de Sitter space S1 (n+1) (1) with constant mean curvature and non negative sectional curvature. It is proved that M is isometric to a hyperbolic cylinder or an Euclidean space if H ≥1. When 2(n-1)^(1.2)/n < H < 1, there exists a complete rotation hypersurfaces which is not a hyperbolic cylinder.