Abstract: The pseudo-parallel space-like hypersurface in Lorentzian product space Mⁿ(c)×R₁ is studied, and the necessary and sufficient conditions for the hypersurfaces to be pseudo-parallel are hence obtained. This proves that the pseudo-parallel hypersurfaces are equivalent to H-parallel hypersurfaces, and proves further that the pseudo-parallel space-like hypersurfaces with three different eigenvalues are constantly-angled hypersurfaces.

Key words: Lorentzian product space, spacelike hypersurface, pseudo-parallel, H-parallel