Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems

Spacelike graphs of constant mean curvature over compact Riemannian manifolds in Lorentzian manifolds with constant sectional curvature are studied. The corresponding Calabi-Bernstein type problems are stated. In the case of nonpositive sectional curvature all their solutions are obtained, and for positive sectional curvature well-known results are extended.