Conformally flat Lorentzian hypersurfaces in R14 with a pair of complex conjugate principal curvatures

A three dimensional Lorentzian hypersurface x:M13→R14 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of R14. Using the projective light-cone model, for those ones whose shape operators have a pair of complex conjugate eigenvalues, we study the integrability condition by constructing a scalar conformal invariant and a canonical moving frame in this paper. It follows that these hypersurfaces can be determined by the solutions to a system of three-order partial differential equations.