Some generalized curves in three dimensional compact lie groups

This study consists of three parts. In the first part, an introduction is given. In the second part, basic definitions and theorems about curves in 3-dimensional Euclidean space and definitions and basic theorems for some special curves are given. Then, definitions of some special curves defined in the literature in 3-dimensional Lie groups with bi-invariant metric and basic theorems about these curves are given. Finally, definitions and theorems about generalized helices in 3-dimensional Lie groups with left-invariant metric are given. The third chapter constitutes the original part of this work. In this work, the Involute-Evolute curves, Bertand and Mannheim curves in 3-dimensional Lie groups with left-invariant metric are defined and firstly the relations between Frenet elements of these curves are investigated. Then, with the help of these relations, some characterizations of these curves are given