Finite type curves in 3-dimensional Sasaki space

The purpose of this study was composed of five parts cylinder, 3 ? dimensional space, the underlying finite Sasaki investigated types of curves. In the first chapter, the introduction has been given and summary of the literature on the subject were made. Basic definitions and concepts have been given in the second chapter. In the third chapter, in R^3 (-3) Sasaki space which has positive definite metric where signature is (+, +, +), and ? ?sectional curvature is equal to ? 3. We have studied finite type curve which lies in cylinders N^2 (c) and N^2 (a,b). In the fourth chapter, for indefinite metric in R^3 (i.e. signature (-, -, +), (+, +, -) and (+, -, +)) we have studied finite type curve which lies in N^2 (c), N^2 (a,b), N_1^2 (c) and N_1^2 (a,b). The obtained results are discussed in the last chapter.