Null Hypersurfaces Of Pseudo Null Curves In Euclidean 4-space With Index 2

The main goal of this paper is to study the issues about singularities of null hypersurfaces of pseudo null curves in semi-Euclidean 4-space with index 2. To do this we construct a null frame and a Lorentz distance-squared function of the pseudo null 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 have obtained some properties of the nullcone Gaussian surface of the pseudo null curve.