Geometry of null Cartan curves and applications

This thesis consist of ve chapters. The first chapter, some basic defi nitions have been presented. In the second chapter, we have been de fined null curves and quasi orthonormal basis along a curve. The third chapter, we have been de fined the Frenet equations and their Frenet frames along a smooth null curve of Lorentzian manifold (M1^m+2,g). We have been given the geometry of null curves in M1^3,M1^4,M1^5 and we have been presented some examples. The fourth chapter we have been presented Cartan Frenet frame with respect to a distinguished parameter for null curve of Lorentzian manifolds and we have been given classi cation of null helices in 3,4,5 dimensional Lorentzian space forms. In the last chapter we have been presented applications of null curves.