A Rigidity Theorem on Spacelike Hypersurfaces in Generalized Robertson–Walker Spacetimes

We study the properties of complete parabolic constant mean curvature spacelike hypersurfaces in generalized Robertson–Walker (GRW) spacetimes I×φPn whose warping function φ fulfills a certain convexity criterion such that −φ is convex, and whose Ricci curvature of the fiber Pn is non-negative. Our approach is based on calculating the Laplacian of an appropriate function. Under appropriate conditions on the constant mean curvature, by using the parabolicity, we obtain a rigidity theorem and some corollaries of spacelike hypersurfaces. As a consequence, we solve new corresponding Calabi–Bernstein-type problems.