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Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems. (English) Zbl 0912.53046
Authors’ abstract: “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”.

##### MSC:
 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
##### Keywords:
GRW space; Einstein space; Ricci tensor; spatially closed
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##### References:
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