Dupin Hypersurfaces in Lorentzian Space forms

Similar to the definition of Dupin hypersurface in Riemannian space forms, we define the spacelike Dupin hypersurface in Lorentzian space forms. As conformal invariant objects, spacelike Dupin hypersurfaces are studied in this paper using the framework of conformal geometry. Further we classify the spacelike Dupin hypersurfaces with constant M\"{o}bius curvatures, which are the partition ratio of the principal curvatures of the spacelike Dupin hypersurface.