Framed osculating and rectifying curves in 4-dimensional Euclidean space

This thesis consists of four chapters. The first chapter is devoted to the introduction. The second chapter is devoted to the basic concepts in Euclidean space. Also in this section, basic definitions and theorems about osculating and rectifying curves in 4-dimensional Euclidean space, the definition of framed curve in 4-dimensional Euclidean space are given. The third and fourth chapters are the original chapters of this thesis. In the third chapter, the framed osculating curve in 4-dimensional Euclidean space, is defined. Then, the conditions of to be framed osculating curve and some characterizations of framed osculating curve are given in 4-dimensional Euclidean space. In the fourth chapter, the framed rectifying curve in 4-dimensional Euclidean space, is defined. Also, the conditions of to be framed rectifying curve and some characterizations of framed rectifying curve are given in 4-dimensional Euclidean space.