Abstract
Abstract A three dimensional Lorentzian hypersurface x : M 1 3 → R 1 4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of R 1 4 . 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.
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