On geometry of the directional null curves in Minkowski space

There have been many studies on null and nonnull curves with Frenet frame and Bishop frame in three-dimensional Minkowski space. The quasi-frame was introduced as an alternative to the frames presented in these studies and it was seen that the quasi-frame can be computed more easily than other frames. The aim of this thesis is to investigate the geometry of directional null and pseudo null curves with the quasi-frame constructed by a projection vector in three-dimensional Minkowski space. This thesis consists of five chapters. Firstly, introduction and objective, literature review about previous researches related to the thesis, and in the third chapter, discussion of the basic definitions and theorems used in our dissertation are presented. The following chapters contain the original part of our thesis. In the fourth chapter, the null quasi-frame and pseudo null quasi-frame are introduced in three-dimensional Minkowski space. Derivative equations, vector products, various theorems and examples of the null quasi-frame and pseudo null quasi-frame are given. Additionally, the relations between the null quasi-frame and the null Frenet frame are identified in this chapter. Finally, the classification of directional null and pseudo null curves is discussed. In the last section, the theorems about directional null and pseudo null Bertrand and Mannheim curve pairs are proved by considering the properties of the curve pairs obtained by using different frames in three-dimensional Minkowski and by using the null and pseudo null quasi-frame structure obtained in the fourth section.