We give a characterization of the n-dimensional (n ≥ 3) hyperbolic cylinders in a Lorentzian space form. We show that the hyperbolic cylinders are the only complete space-like hypersurfaces in an (n + 1)-dimensional ...

Space-like submanifolds, with dimension greater than three and with negative definite normal bundle in a general de Sitter space, of any index, are studied. For the compact space-like submanifolds whose mean curvature has ...