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Several uniqueness results for non-compact complete stationary spacelikesurfaces in an $n(\geq 3)$-dimensional Generalized Robertson Walker spacetimeare obtained. In order to do that, we assume a natural inequality involving theGauss curvature of the surface, the restrictions of the warping function andthe sectional curvature of the fiber to the surface. This inequality gives theparabolicity of the surface. Using this property, a distinguished non-negativesuperharmonic function on the surface is shown to be constant, which impliesthat the stationary spacelike surface must be totally geodesic. Moreover,non-trivial examples of stationary spacelike surfaces in the four dimensionalLorentz-Minkowski spacetime are exposed to show that each of our assumptions isneeded.

Complete stationary spacelike surfaces in an $n$-dimensional Generalized Robertson-Walker spacetime