Surfaces with constant mean curvature along a given curve in 3-dimensional lie groups

In this study, sufficient conditions are obtained for surfaces with constant mean curvature in 3-dimensional Lie groups. Some examples are given to support the results obtained. This study consists of five chapters. The first chapter, is devoted to the introduction. In the second part, basic definitions and theorems related to 3-dimensional Euclidean space and Lie group are given. The third part and beyond constitutes the original part of the thesis. In this section, conditions are obtained to find surfaces whose mean curvature is constant along a given curve in Lie group. In the fourth part conditions are obtained and examples are created to find surfaces with constant mean curvature along Smarandache curves in terms of the Frenet frame of the curve given in the 3-dimensional Lie group. In the fifth part, conditions are obtained to find surfaces with a constant mean curvature and passing through a given curve according to the alternative {N,C,W} frame in the 3-dimensional Lie group.