Singularities Of Indefinite Hypersurfaces And Indefinite Surfaces Along Timelike Curves In Nullcone With Index Two

In this thesis,a class of indefinite hypersurfaces and a class of indefinite sur-faces,generated by timelike curves that located in nullcone in 4-dimensional semi-Euclidean space with index 2 are discussed.Set up clear theoretical framework of differential geometry on space curve in R24.Using the unfolding theory in singularity theory,the singularities of the indefinite hypersurfaces and the indefinite surfaces are classified and the different kinds of singularities are estimated by means of a ge-ometric invariant.Meanwile,the definition of osculating nullcone is presented,the study shows that the differential geometric invariant σ of timelike curves measured also the order of the contact between a timelike curve and a osculating nullcone.To better illustrate our results,we give an example of the indefinite hypersurface and the indefinite surface.