| In this paper,as applications of unfolding theory in singularity theory,we investigate the singularities of five special Lorentzian Darboux surfaces generated by a regular curve lying on a spacelike hypersurface in Lorentz-Minkowski 4-space,using two kinds of extended Lorentzian Darboux frames along the curve as tools.At the same time,we define five special Lorentzian Darboux surfaces and receive the singularity classification results of five special surfaces.Meanwhile,five new invariants are obtained to characterize the singularities of five special surfaces and their geometric meanings are discussed in detail.In addition,some dual relationships between a normal curve of the original curve and five Lorentzian Darboux surfaces are revealed under the meanings of Legendrian duality. |
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