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In this paper, we study complete hypersurfaces with constant mean curvature in anti-de Sitter space H n+1 1(-1). we prove that if a complete space-like hypersurface with constant mean curvature x: M → H n+1 1(-1) has two distinct principal curvatures λ, μ, and inf{pipe}λ - μ{pipe} > 0, then x is the standard embedding H m×H n-m in anti-de Sitter space H n+1 1(-1). © 2012 Springer-Verlag.

An application of maximum principle to space-like hypersurfaces with constant mean curvature in anti-de Sitter space