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In this paper, we study closed -maximal spacelike hypersurfaces in anti-de Sitter space with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
We transform the problem of determining isometric immersions from into into that of solving equations of degenerate Monge-Ampère type on the unit ball . By presenting one family of special solutions to the equations, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set.
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