In this paper, we first set up an alternative fundamental theory of M?bius geometry for any umbilic-free spacelike hypersurfaces in four dimensional Lorentzian space form, and prove the hypersurfaces can be determined...In this paper, we first set up an alternative fundamental theory of M?bius 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 {E_i}. Then we give a complete classification for spacelike M?bius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either M?bius 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 M?bius form.展开更多
基金supported by NSFC(Grant Nos.11571287 and 11671330)supported by NSFC(Grant Nos.11331002 and 11471021)
文摘In this paper, we first set up an alternative fundamental theory of M?bius 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 {E_i}. Then we give a complete classification for spacelike M?bius homogeneous hypersurfaces in four dimensional Lorentzian space form. They are either M?bius 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 M?bius form.
