Singularities of null hypersurfaces of pseudonull curves

The main goal of this paper is to study the singularities of null hypersurfaces of pseudonull curves. to do this we construct a null frame and a lorentz distance-squared function of the pseudonull curve. the relations are shown between singularities of the null hypersurfaces and those,of the lorentz distance-squared function. and we reveal the geometric meanings of the singularities of such hypersurfaces. in addition,we also introduce some properties of the nullcone gaussian surface of the pseudonull curve. © 2015 xiupeng cui and donghe pei.