The Gauss map of timelike surfaces in \(\mathbb{R}_ 1^ n\) (Q1899642)

The author obtains a necessary and sufficient condition for a map \(G : D \to G^*_{2,n}\) to be the Gauss map of a timelike surface \(S\) in \(\mathbb{R}^n_1\), where \(D\) is a simply connected domain in \(\mathbb{R}^2_1\) or a simply connected 2-dimensional Lorentzian manifold. A counterexample shows that a nonminimal timelike surface in \(\mathbb{R}^n_1\) cannot be essentially determined by its Gauss map.