Uniqueness of complete maximal surfaces in certain Lorentzian product spacetimes

We considered complete maximal surfaces in a Lorentzian manifold given by the product of the negative definite real line and a 2-dimensional Riemannian manifold, such that the Gauss curvature of the Riemannian fiber is bounded from below. The main purpose of this work is to characterize the surfaces satisfying a comparison involving the height function and the shape operator as slices. In order to obtain the results, we developed a proper extension of a classical result by Nishikawa, for the Ricci bounds depending on the distance function. Finally, we present non-trivial examples of surfaces to emphasize the necessity of the assumptions we required in our results.