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A geometrical correspondence between maximal surfaces in anti-De Sitterspace-time and minimal surfaces in the Riemannian product of the hyperbolicplane and the real line is established. New examples of maximal surfaces inanti-De Sitter space-time are obtained in order to illustrate thiscorrespondence.

A geometrical correspondence between maximal surfaces in anti-De Sitter space-time and minimal surfaces in $\mathbb{H}^2\times \mathbb{R}$