Abstract
Our primary object of this paper is to give a representation formula for constant mean curvature spacelike surfaces (including maximal surfaces) in the anti-de Sitter 3-space H 3 1(c 2) of constant negative curvature c 2, similar to the Kenmotsu type representation formula for nonzero constant mean curvature spacelike surfaces in the Minkowski 3-space L 3. This formula implies that every simply connected spacelike surface M with constant mean curvature in H 3 1(c 2) can be represented by a harmonic map from M to the hyperbolic 2-plane H 2.
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