Spacelike Möbius Hypersurfaces in Four Dimensional Lorentzian Space Form

In this paper, we first set up an alternative fundamental theory of Mobius geometry for any umbilic-free spacelike hypersurfaces in four dimensional Lorentzian space form, and prove the hypersurfaces can be determined completely by a system consisting of a function W and a tangent frame {Ei}. Then we give a complete classification for spacelike Mobius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either Mobius equivalent to spacelike Dupin hypersurfaces or to some cylinders constructed from logarithmic curves and hyperbolic logarithmic spirals. Some of them have parallel para-Blaschke tensors with non-vanishing Mobius form.