On curve motions in Euclidean and non-Euclidean spaces

This thesis consists of six chapters. The first chapter is devoted to the introduction. In the second chapter, Euclidean 3-space, Lorentz an 3-space, Galilean 3-space and their properties are mentioned respectively. In the third chapter helicoidal surfaces, which are the trajectories of the curves under the helicoidal motions in 3 dimensional Euclidean space, are examined, and the theorems about the mean curvatures of the surfaces and Gaussian curvatures are given. In the fourth chapter, helicoidal motions in 3 dimensional Lorentz Space is decomposed and curvatures for surfaces obtained with the motion groups are mentioned. In the fifth chapter, motions of curves in 3 dimensional Galilean space are examined, and curvature calculations are made for rotating surfaces. Finally, the sixth chapter is devoted to discussion and conclusions.