Characterizations of helices and slant helices according to quaternionic frame

This study consists of five chapter.In the first chapter, basic concepts of Euclidean space and set of quaternions are mentioned. Also in this chapter, some basic definitions and theorems of helices are given.In the second chapter, the definition of quaternionic slant helix is given and some characterizations of them are investigated in the 3- dimensional and 4- dimensional Euclidean spaces and .In the thirth chapter, quaternionic general helix is defined and some integral characterizations of them are investigated in the 4- dimensional Euclidean space .In the fourth chapter, the definition of quaternionic slant helix is given and some integral characterizations of them are investigated in the 4- dimensional Euclidean space .Finally, in the fifth parth, a summary of the study is given and suggestions are proposed for investigations in future.The second, thirth and fourth chapters are the original parts of this thesis.