The geometry of some special curves in semi-Riemannian spaces

This work consists of four chapters. In the first chapter, the basic concepts of differential geometry relating to the subjects in the main chapters of this thesis areintroduced.In the second chapter, a new idea of Bertrand curves is presented. Abiding by this idea the conditions are investigated for a null curve to be a Bertrand curve. After that, null spherical curves in R^5-1 are characterized by their curvature functions. Finally in this chapter, we obtained a classification of Bertrand curves in R^3-1 and R^4-1.In the third chapter, by using the same notion of Bertrand curve in the second chapter, we established the conditions for a spacelike curve in R^4-1 so that it would be a Bertrand curve.In the last chapter, null Bertrand curves in a low dimensional pseudo-Euclidean space of index two and null spherical curves in R^n-2 are determined. After defining the evolute of a null curve and the involute of a spacelike curve in R^6-2, a correspondence between them which is similar to that between the plane evolute and the involute is shown.