On parallel curves in 3-dimensional compact lie groups

This thesis consists of four parts. The first party is devoted to the introduction. In the second party, basic concepts in 3-dimensional Euclidean space and basic information about curves are given and some special curves are examined. Then, basic information about Lie algebra and Lie group basic concepts and curves were given and special curves such as helix, involüt-evolüt, Bertrand, Mannheim, Smarandache, were examined. In the third part, inspired by these special curves examined in the Lie group, the definitions of the parallel curve in the vector direction, the parallel curve in the direction of the vector,, and the parallel curve in the direction of the vector, which is the linear combination of the and vectors of a curve according to the Frenet frame, are given and characterized. Finally, some theorems were obtained by finding the Frenet elements of these curves. In the fourth party, a tabular summary of our obtained theorems is created.