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Let M be a connected space-like surface in a Lorentzian space form  M 4 1 (c). We define a time-like hypersurface M ∗ which is the image of a subbundle of the normal bundle of a space-like surface M spanned by a time-like unit normal vector field ξ on M in a 4-dimensional Lorentzian space form  M 4

Time-like hypersurfaces of 4-dimensional Lorentzian space forms with zero mean curvature